Slope-Intercept Form(Week 5 Day 1)

Casie CroffKristy ChimeraNichole Oswald

Title: Slope-Intercept FormGrade: 9th

Section 5.3 Slope-Intercept FormMaterials: calculators, worksheets, chalkboard/whiteboard, chalk/markers**ALL WORKSHEETS WILL BE PROVIDED

Lesson Overview: Students will learn to write equations of a line in slope-intercept form, when given the slope and y-intercept or a graph containing 2 points. They will also be able to graph an equation in standard form.

Lesson Objectives:Students will be able to write equations in slope-intercept form, and identify the parts of the equation (slope, y-intercept). [Application]Students will be able to transform an equation into standard form and then graph it. [Analysis]Given a word problem the students will be able to create an equation from the information, graph the line, and then answer questions based on their graphs and equations. [Evaluation]

NYS Standards:Key Idea 3: Operations- Use addition, subtraction, multiplication, division, and exponentiation with real numbers and algebraic expressions.Key Idea 5: Measurement- Relate the slope of a line to the coordinate plane.Key Idea 7: Patterns and Functions- Represent and analyze functions, using verbal descriptions, tables, equations, and graphs.

Anticipatory Set: (5 minutes)Pass out “Bring on the FUN-ctions” worksheet. Students should complete this independently, and then go over the answers as a class. This is a brief practice reviewing slope (m=) and the y-intercept.

Developmental Activity: (25 minutes)1.) Pass out the “Everything You Ever Wanted to Know About Slope-Intercept

Form” worksheet.2.) Briefly review the definition of slope and introduce the formal definition of y-

intercept.3.) Complete the worksheet with all of the examples.4.) Be sure to discuss each answer as a group.

Closure: (5 minutes)Discuss what they learned about slope-intercept form. What does the m and b represent in the equation?

Assessment: (7 minutes) This totals 42 minutes – there are only 40!Have the students complete the Exit Ticket and hand it in before they leave. This will be graded.

Name: Date:“Bring on the FUN-ctions”

1.) What is the slope (m =?) of this line? _________At what point does it cross the y-axis? _________

6

4

2

-2

-4

-6

-8

-10

-10 -5 5 10 15

2.) What is the slope (m =?) of this line? _________ At what point does it cross the y-axis? _________

6

4

2

-2

-4

-6

-10 -5 5 10

Name: Teacher Copy Date:

“Everything You Ever Wanted to Know About Slope-Intercept Form”

Slope: describes how steep the line is and is the ratio of rise over run.

Did you know that the point where a line crosses the y-axis has a special name?

Well, it does and that special name is y-intercept.When you look at any graph of any line that crosses the y-axis, what is the x-value of that point? ZeroTherefore the y-intercept is just the y-value of that point. It is labeled b in the picture below.

We know that the slope is represented by m and the y-intercept is represented by b. Now we are able to write the equation of a line in general:

y=mx+b: this is called SLOPE-INTERCEPT FORM

1.) Write the equation of a line whose slope is -1 and whose y-intercept is 2.y= -1x + 2 ……y= -x +2

2.) Write the equation of a line whose slope is 2 and whose y-intercept is -3.y= 2x – 3

3.) Write an equation of the line shown in the graph.6

4

2

-2

-4

-6

-10 -5 5 10

X

Y

(2,-1)

(0,3)

First we need to find the slope.

(x1,y1) (0,3) and

(x2,y2) (2, -1)

m 1 32 0

m= -2

Y

X

(0,b)

Where does the line cross the y-axis? (0,3)Therefore, the y-intercept is 3.Now write the equation: y = -2x+3

4.) Graph the equation: y= 2x-3.Slope = 2Y-intercept = -3

6

4

2

-2

-4

-6

-10 -5 5 10

5.) Write the equation 4x-3y = 3 in standard slope-intercept form.What do we want to solve for? y

4x- 3y = 3-3y = 3 – 4x

y 53

x 2

6.) A candle is 6 inches tall and burns at a rate of

12

inch per hour.

Write a linear equation in slope-intercept form to model the situation.

Y= -

12

x +6

Graph the equation:8

6

4

2

-2

-4

-5 5 10

Time

Height

Looking at your graph, how long will it take the candle to completely burn out?12 hours

Name: Date:

“Everything You Ever Wanted to Know About Slope-Intercept Form”

Slope: _______________________________________________________

Did you know that the point where a line crosses the y-axis has a special name?

Well, it does and that special name is _____________.When you look at any graph of any line that crosses the y-axis, what is the x-value of that point? _________Therefore the y-intercept is just the y-value of that point. It is labeled b in the picture below.

We know that the slope is represented by___ and the y-intercept is represented by __. Now we are able to write the equation of a line in general:

__________: this is called SLOPE-INTERCEPT FORM

1.) Write the equation of a line whose slope is -1 and whose y-intercept is 2.

2.) Write the equation of a line whose slope is 2 and whose y-intercept is -3.

7.) Write an equation of the line shown in the graph.6

4

2

-2

-4

-6

-10 -5 5 10

X

Y

(2,-1)

(0,3)

First we need to find the slope.

(x1,y1) (0,3) and

(x2,y2) (2, -1)Where does the line cross the y-axis? _______

Y

X

(0,b)

Therefore, the y-intercept is ___.Now write the equation: _____________

8.) Graph the equation: y= 2x-3.Slope = __Y-intercept = __

6

4

2

-2

-4

-6

-8

-10 -5 5 10

9.) Write the equation 4x-3y = 3 in standard slope-intercept form.What do we want to solve for? ___

10.) A candle is 6 inches tall and burns at a rate of

12

inch per hour.

Write a linear equation in slope-intercept form to model the situation.

Graph the equation:

6

4

2

-2

-4

-6

-8

-10 -5 5 10

Looking at your graph, how long will it take the candle to completely burn out?

Name: Date:Exit Ticket

1.) Graph the equation y = -3x+16

4

2

-2

-4

-6

-8

-10 -5 5 10

2.) Write the equation 2x + 3y = 6 in standard (Remove the word “standard”) slope- intercept form.

Writing Equations in Slope-Intercept Form(Week 5 Day 2)

Kristy ChimeraCasie Croff

Nichole Oswald

Title: Writing Equations in Slope-Intercept FormGrade 10

Materials:Chalkboard or whiteboardChalk or whiteboard markersWorksheets (I will have enough copies for everyone!)Graphing Calculator

Lesson Overview: Students will learn how to find the equation of a line given one point and the

slope, and also when given two points and no slope. Students will also learn how to check their answers two different ways: one by using the graphing calculator, and the other by plugging in the point that they did not use (when given two points).

Objectives:The student will be able to apply the slope formula to find a slope when given two points (application).The student will be able to generate an equation of a line when given required information (synthesis).The student will be able to distinguish what information is given in a word problem (analysis).

NYS Standards:Key Idea 1: Mathematical Reasoning-students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.Key Idea 3: Operations-students use mathematical operations and releationships among them to understand mathematics.

3A. Use addition, subtraction, multiplication, division, and exponentiation with real numbers and algebraic expressions.

Key Idea 7: Patterns/Functions-students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.

7A. Represent and analyze functions, using verbal descriptions, tables, equations, and graphs.7D. Model real-world situations with the appropriate function.

Anticipatory Set: (5 minutes)Hand out the worksheet titled “Review of graphing”. Have the students complete

the worksheet independently at their seats (3 minutes). As the students are working, walk around the room to do an assessment of the students’ prior knowledge. Once the students are done with the worksheet, bring the class together and quickly go over the parts that students were missing (have the students explain their answers and how they reached them). (2 minutes). Explain to the students that today we will be learning how to write equations in Slope-Intercept form.

Developmental Activity: (18 minutes)1. Hand out the guided notes titled “Equations in slope-intercept form”.2. Go through example one as a class, asking the students for ideas for each step

of the process. Maybe have students come up to the board to complete the different steps. (4 minutes)

3. Do the same with example two. Ask the students why they can’t just “plug and chug” into y=mx+b before they find the slope. (7 minutes)

4. Work through example three as a class. Have the students come up with what each step is (step 1: explore, step 2: plan, step 3: solve, step 4: examine). (7 minutes)

Guided Practice: (10 minutes) Have the students work in groups of 2 to complete the practice problems in their guided notes. Walk around the room and help students if they are stuck (8 minutes). Briefly go over the answers to the problems with the class (2 minutes).

Closure: (2 minutes) Briefly review the steps involved in each kind of problem (when given one point and the slope, and when given only two points and no slope). Ask the students what each step includes.

Independent Practice: (5 minutes) Pass out the exit slip. Give the students approximately 5 minutes to complete the exit slip. This will be for a homework grade and will be collected before they leave the room!

Name:__________________________________________ Date:_____________

Review of Graphing

Directions: Plot and label the following points on your graph. DO NOT connect the points!

A (1,0) B (2,4) C (-2,-2) D (-3,4) E (5,-1) F (0,0)

How did you know where to put A on your graph? ________________________________________________________________________________________________________________________________________________

Write the slope formula: m = __________

The equation of a line in slope-intercept form is: y = mx + b

Look at the equation above. Match each variable with what it represents. Remember this is NOT for a grade. Make your best educated guess!

y ___________ 1) Slope

x ___________ 2) Y-value

m ___________ 3) Y-intercept

b ___________ 4) X-value

Name:______Answer Key__________________________ Date:_____________

Review of Graphing

Directions: Plot and label the following points on your graph. DO NOT connect the points!

A (1,0) B (2,4) C (-2,-2) D (-3,4) E (5,-1) F (0,0)

How did you know where to put A on your graph? My x-value is 1, so I go to the right 1 from the origin. Also, my y-value is 0, so I do not have to move up or down from the origin.

Write the slope formula: m = 1212

xxyy

−−

The equation of a line in slope-intercept form is: y = mx + b

Look at the equation above. Match each variable with what it represents. Remember this is NOT for a grade. Make your best educated guess!

y ____2______ 1) Slope

x ____4______ 2) Y-value

m ___1______ 3) Y-intercept

b ____ 3__ ___ 4) X-value

Name:____________________________________________ Date:_____________

Equations in Slope-Intercept Form

Example 1: Using the slope-intercept form, write an equation of a line that passes through point (1,5), with slope 2.

Step 1:We need to know values for y, x, m, and b. Which values are given to us?

y = _____ x = _____ m = _____ b = _____

What do we need to find? _______

Step 2: Solve the equation y = mx + b for the variable we are missing, by plugging in the number that we DO know.

So our missing variable ____ is ____.

Step 3: An equation of a line that goes through point (1,5) with slope 2 is: ___________

Check your work with your graphing calculator!Step 1: Go to your y = menuStep 2: In Y1 write 2x + 3Step 3: Press Zoom 0 (Zoom Fit)Step 4: Press the Trace buttonStep 5: Find the point (1,5). If the point is on the line, then the equation is correct!

Does our equation work? _________________________________________________________________________________

Example 2: What about when you are given 2 points but no slope? Find an equation of the line that passes through points (-3,-1) and (6,-4).

Step 1: What values do we know? y = _____ x = _____ m = _____ b = _____

What do we need to find? _____________ and _____________

Can we just “plug and chug” into y = mx + b to find b? ________. Why? _____________

First we need to find out what the slope is! Using the slope formula, plug in x1, x2, y1, and y2 to find the slope.

Step 2: Slope = 1212

xxyy

= = =

Now can we “plug and chug” into y = mx+b to find b? ________

Step 3:

So we have y = _____ x = _____ m = _____ b = _____

Step 4: So our equation of a line that passes through points (-3,-1) and (6,-4) is:

__________________________________

Check this on your graphing calculator the same way as example 1. Does it work? _____________________________________________________________________________

Example 3: In the middle of the 1998 baseball season, Mark McGwire seemed to be on track to break the record for most runs batted in. After 40 games, McGwire had 45 runs batted in. After 86 games, he had 87 runs batted in. Write a linear equation to estimate the number of runs batted in for any number of games that season.

Step 1: __________: What do we know? ______________________________________

Step 2: __________: Let _____ = ____________________________________________

Let _____ = ____________________________________________

So all we need to do is write an equation of the line that passes through ( , ) and ( , ).

Step 3: __________ What do we need to find before we can “plug and chug”? ________

So, Slope = 1212

xxyy

= = =

Now we can “plug and chug” to find _____.

So our equation to estimate the number of runs batted in for any number of games this

season is:_________________________________________________

Step 4: __________ : Check your result by substituting the coordinates of the point not

chosen into the equation. Does it work? _____

________________________________________________________________________

Practice Problems: Use the back of this paper if necessary. Be sure to show your work!!!

1. Find an equation of a line that passes through point (2, 4) with slope 5.

2. Find an equation of a line that passes through points (1, 6) and (3, 8).

Name:________Answer Key__________________________ Date:_____________

Equations in Slope-Intercept Form

Example 1: Using the slope-intercept form, write an equation of a line that passes through point (1,5), with slope 2.

Step 1:We need to know values for y, x, m, and b. Which values are given to us?

y = __5___ x = __1___ m = __2___ b = __?___

What do we need to find? ____b___

Step 2: Solve the equation y = mx + b for the variable we are missing, by plugging in the number that we DO know.

y = mx + b5 = 2(1) + b5 = 2 + b

-2 -2 3 = b

So our missing variable _b___ is __3__.

Step 3: An equation of a line that goes through point (1,5) with slope 2 is: _y = 2x + 3

Check your work with your graphing calculator!Step 1: Go to your y = menuStep 2: In Y1 write 2x + 3Step 3: Press Zoom 0 (Zoom Fit)Step 4: Press the Trace buttonStep 5: Find the point (1,5). If the point is on the line, then the equation is correct!

Does our equation work? __Yes____________________________________________________________________________

Example 2: What about when you are given 2 points but no slope? Find an equation of the line that passes through points (-3,-1) and (6,-4).

Step 1: What values do we know? y = -1 or -4 x = -3 or 6 m = _?____ b = __?___

What do we need to find? _m and b. The slope and the y-intercept

Can we just “plug and chug” into y = mx + b to find b? _no___. Why? _We do not know enough of the variables .

First we need to find out what the slope is! Using the slope formula, plug in x1, x2, y1, and y2 to find the slope.

Step 2: Slope = 1212

xxyy

= = = 31

Now can we “plug and chug” into y = mx+b to find b? __Yes!__

Step 3:y = mx + b-4 = (-1/3)(6) + b-4 = -2 + b+2 +2-2 = b

So we have y = _-4____ x = _6____ m = _-1/3____ b = __-2___

Step 4: So our equation of a line that passes through points (-3,-1) and (6,-4) is:

___y = (-1/3)x -2______________

Check this on your graphing calculator the same way as example 1. Does it work? _Yes!_________________________________________________________________________

Example 3: In the middle of the 1998 baseball season, Mark McGwire seemed to be on track to break the record for most runs batted in. After 40 games, McGwire had 45 runs batted in. After 86 games, he had 87 runs batted in. Write a linear equation to estimate the number of runs batted in for any number of games that season.

Step 1: _Explore: What do we know? Number of runs after 40 and 86 games .

Step 2: Plan____: Let _x____ = _number of games . _________________

Let _y____ = __number of runs batted in.____

So all we need to do is write an equation of the line that passes through (40,45) and (86,87).

Step 3: Solve : What do we need to find before we can “plug and chug”? _Slope!_

So, Slope = 1212

xxyy

= = = 0.91

Now we can “plug and chug” to find _b___.

y = mx + b or y = mx + b Extend the decimal places 87 = 0.91(86) + b 45 = 0.91(40) + b to end up with the same 87 = 78.26 + b 45 = 36.4 + b values for b! -78.26 -78.26 -36.4 -36.4 8.74 = b 8.6 = b

So our equation to estimate the number of runs batted in for any number of games this

season is:_y = 0.91x + 8.74 or y = 0.91x + 8.6____

Step 4: Examine : Check your result by substituting the coordinates of the point not

chosen into the equation. Does it work? Yes

________________________________________________________________________

Practice Problems: Use the back of this paper if necessary. Be sure to show your work!!!

3. Find an equation of a line that passes through point (2, 4) with slope 5.

y = 4 x = 2 m = 5 b = ?

y = mx + b4 = 5(2) + b so our equation is y = 5x -64 = 10 + b

-10 -10-6 = b

4. Find an equation of a line that passes through points (1, 6) and (3, 8).

Slope = (y2-y1) / (x2-x1) = (8-6) / (3-1) = 2/2 = 1 So the slope is 1.

y = mx + b or y = mx + b so our equation is:6 = 1(1) + b 8 = 1(3) + b y = 1x + 5

6 = 1 + b 8 = 3 + b or -1 -1 -3 -3 y = x + 5

5 = b 5 = b

Name: ___________________________________________ Date:_____________

Exit Ticket: SHOW ALL WORK!!!!!

1. Write an equation of the line that passes through point (4,-2) with slope 2.

2. What is the y-intercept? _______________________________________________

__________________________________________________________________

Name: _____Answer Key_______________________________ Date: _____________

Exit Ticket: SHOW ALL WORK!!!!!

1. Write an equation of the line that passes through point (4,-2) with slope 2.

y = -2 x = 4 m = 2 b = ?

y = mx + b-2 = 2 (4) + b so our equation is y = 2x – 10-2 = 8 + b-8 -8-10 = b

2. What is the y-intercept? ___The point where the line crosses the y-axis .

__________________________________________________________________

Writing Equations in Point-Slope Form(Week 5 Day 3)

Casie CroffKristy ChimeraNichole Oswald

Title: Writing Equations in Point-Slope Form

Topic: Point-Slope Form of Linear Equations

Grade: Algebra (Grades 9-12)

Materials:Students: Pen/Pencil

Worksheet

Teacher: Worksheets (I will provide copies for all groups.)

Lesson Overview: Students will learn how to write a linear equation in point-slope form using the slope formula. Students will write linear equations in different forms (standard, slope-intercept, and point-slope). Students will determine equivalences between equations using point-slope form with different points.

Learning Objectives:Students will be able to generate and write linear equations in point-slope form, as well as, standard form and slope-intercept form.Students will derive the point-slope from of linear equations using previous knowledge of the slope formula.Students will compare and contrast the different forms of linear equations to determine equivalences.

NYS Learning Standards:Key Idea 3: Operations3A: Use addition, subtraction, multiplication, division, and exponentiation with real numbers and algebraic expressions.Key Idea 5: Measurement5G: Relate absolute value, distance between two points, and the slope of a line to the coordinate plane.Key Idea 7: Patterns/Functions7A: Represent and analyze functions, using verbal descriptions, tables, equations, and graphs.

Anticipatory Set: (5 minutes)Pass out “Let’s Review” Worksheet to all students.Students will complete the multiple choice questions.Teacher should circulate amongst the students to ensure they are on task and not struggling.Teacher will go over answers by reading question aloud and asking students for answer.

Developmental Activity: (25 minutes)Pass out “Writing Equations in Point-Slope Form” Worksheet to all students.Write slope formula and given points for “Think About It” Activity on the board. Have students lead you through solving the slope formula until you’ve reached the point-slope form of the linear equation.Explain to students what they’ve just derived/found.Complete guided notes and examples with students having students lead you through the examples.Divide students into 2 groups. Pass out “Who’s Right?” Worksheet to the groups.Each group will complete the equations on the worksheet.Teacher will then ask for a presenter for each problem to discuss the group’s findings and conclusions.Teacher will have students compare the 2 equations for similarities and differences.Ask students “So…who’s right?”If students don’t see the equivalence of the 2 equations, have them write the equation in standard or slope-intercept form to make it visible to them that the equations are equivalent. If a student does notice the equivalence, ask them to explain their reasoning / understanding with the class.Ask students what they can conclude from the activity.

Closure: (5 minutes)Complete the “Concept Summary” section of the guided notes.Ask students for information necessary to complete the table.

Assessment: (5 minutes)Pass out “Exit Ticket” Worksheet to all students.Students are to complete the exit ticket and turn it in prior to leaving the class.

Name: ___________________________ Date: ________________Let’s Review

1. The steepness of a line is equal to: a. the horizontal change b. the sideways change c. the vertical change the vertical change the vertical change the horizontal change

2. What x-value does a y-intercept have? a. 1 b. the same as the y-value c. 0

3. How is a y-intercept of 5 written? a. (0,5) b. (5,0) c. (5,5)

4. You can find the slope of a line by calculating: a. the change in y b. the change in x c. the change in x the change in x the change in y the change in x

5. The y-intercept is the y-coordinate where the graph crosses the: a. x-axis b. origin c. y-axis

6. What is the slope of a line containing (0,-6) and (4,0)? a. 1/3 b. 3/3 c. 3/2

Name: ANSWER KEY Date: ________________Let’s Review

1. The steepness of a line is equal to: a. the horizontal change b. the sideways change c. the vertical change the vertical change the vertical change the horizontal change

2. What x-value does a y-intercept have? a. 1 b. the same as the y-value c. 0

3. How is a y-intercept of 5 written? a. (0,5) b. (5,0) c. (5,5)

4. You can find the slope of a line by calculating: a. the change in y b. the change in x c. the change in x the change in x the change in y the change in x

5. The y-intercept is the y-coordinate where the graph crosses the: a. x-axis b. origin c. y-axis

6. What is the slope of a line containing (0,-6) and (4,0)? a. 1/3 b. 3/3 c. 3/2

Name: _______________________ Date: ________________Writing Equations in Point-Slope Form

Think About It!How can you use the slope formula to write an equation of a line?The graph shows a line with slope 2 that passes through (3,4). Another point on this line is (x,y).

The linear equation is written in __________-__________ form, where is a given point on a non-vertical line and m is the __________ of the line.

Example 1: Write the point-slope form of an equation for a line that passes through (-1,5) with slope -3.

Write this equation in standard form. Check your answer.

Write this equation in slope-intercept form.

Example 2Write the point-slope from of an equation for a horizontal line that passes through (6,-2).

NOTE: Vertical lines cannot be written in point-slope form because the slope is undefined. However, since the slope of a horizontal line is 0, horizontal lines can be written in point-slope form.

Example 3a. Write the point-slope form of an equation for a line that passes through the point (1,3) with slope -2.

b. Solve the equation for the domain { -2, 0, 1, 3} x y = -2x + 5 y (x,y)

-2      

0      

1      

3      

c. Graph the solution.                                                                                                                                                                                                                                                                                                                                                                                          

Concept Summary: Forms of Linear Equations

Form Equation Description

Slope - Intercept y = _____ is the slope and b is the _________

__________ - Slope   m is the slope and is a given point

  Ax + By = C

A and B are not both zero. Usually A is nonnegative and A, B, and C are

integers whose greatest common factor is 1.

Name: ________________________ Date: ______________Exit Ticket

Write the point-slope form of a line that passes through the point (3,8) with slope m=2.Show all work!

Write this equation in slope-intercept form.Show all work!

Identify the slope and y-intercept of the equation above.slope: _________________y-intercept: _____________

Name: ANSWER KEY Date: ______________Exit Ticket

Write the point-slope form of a line that passes through the point (3,8) with slope m=2.Show all work!

y - y1 = m (x - x1)y – 8 = 2 (x – 3)

Write this equation in slope-intercept form.Show all work!

y – 8 = 2 (x – 3)y – 8 = 2x – 6y = 2x – 6 + 8y = 2x +2

Identify the slope and y-intercept of the equation above.slope: m = 2y-intercept: (0,2)

Name: _________________________ Date: _____________

Who’s Right?

Tanya and Akira wrote the point-slope form of an equation for a line passing through (-2,-6) and (1,6). Tanya says that Akira’s equation is wrong. Akira says they are both correct. Who is correct? Explain.

Tanya Akira

y + 6 = 4 (x + 2) y – 6 = 4 (x – 1)

Name: ANSWER KEY Date: _____________

Who’s Right?

Tanya and Akira wrote the point-slope form of an equation for a line passing through (-2,-6) and (1,6). Tanya says that Akira’s equation is wrong. Akira says they are both correct. Who is correct? Explain.

Tanya Akira

y + 6 = 4 (x + 2) y – 6 = 4 (x – 1)y + 6 = 4x +8 y – 6 = 4x – 4y = 4x + 8 – 6 y = 4x – 4 + 6

y = 4x + 2 y = 4x + 2

So who’s right?They are both correct.

What can we conclude?Linear equations in point-slope form can be written in slope-intercept form or standard

form.The point-slope forms of equations of different points on the same line are equivalent.

(i.e. You can use different points from the same line and come up with a different point-slope form for each, but when rewritten in standard or slope-intercept form, the equations

are the same.)

Name: ANSWER KEY Date: ________________Writing Equations in Point-Slope Form

Think About It!How can you use the slope formula to write an equation of a line?The graph shows a line with slope 2 that passes through (3,4). Another point on this line is (x,y).

The linear equation is written in point-slope form,

where is a given point on a non-vertical line and m is the slope of the line.

Example 1: Write the point-slope form of an equation for a line that passes through (-1,5) with slope -3.

Write this equation in standard form.

y – 5 = -3 (x + 1) Check: Use point (-1,5)y – 5 = -3x – 3 y + 3x = 2y + 3x – 5 = -3 5 + 3(-1) = 2y + 3x = -3 + 5 5 – 3 = 2y + 3x = 2 or 3x + y = 2 2 = 2 Yes! This is correct.

Write this equation in slope-intercept form.

y + 3x = 2y = 2 – 3xy = -3x + 2

Example 2Write the point-slope from of an equation for a horizontal line that passes through (6,-2).

NOTE: Vertical lines cannot be written in point-slope form because the slope is undefined. However, since the slope of a horizontal line is 0, horizontal lines can be written in point-slope form.

Example 3a. Write the point-slope form of an equation for a line that passes through the point (1,3) with slope -2.

y – 3 = -2(x – 1)

b. Solve the equation for the domain { -2, 0, 1, 3}x y = -2x + 5 y (x,y)

-2 (-2 * -2) + 5 = 4 + 5 9 (-2,9)

0 (-2 * 0) + 5 = 0 + 5 5 (0,5)

1 (-2 * 1) + 5 = -2 + 5 3 (1,3)

3 (-2 * 3) + 5 = -6 + 5 -1 (3,-1)

c. Graph the solution.

Concept Summary: Forms of Linear Equations

Form Equation Description

Slope - Intercept y = mx + b m is the slope and b is the y-intercept

Point - Slope 

m is the slope and is a given point

 Standard Ax + By = C

A and B are not both zero. Usually A is nonnegative and A, B, and C are

integers whose greatest common factor is 1.