SWBAT… Write and graph lines in slope-intercept form Mon, 11/14

Agenda1. WU (10 min)2. Video on graphing (5 min)3. Graphing lines (10 min)4. Writing equations of lines in slope-intercept form

Warm-Up: Solve each equation for y:1. 2y = 4x + 22. -3y = -9x – 123. 21x – 7y =144. 2y + 26 = -6x

HW5: Writing and graphing equations in slope-intercept form

When an equation is in slope-intercept When an equation is in slope-intercept form:form:

When an equation is in slope-intercept When an equation is in slope-intercept form:form:

What is the slope? ____________

2 1y x Now look at the equation below……

What is the y-intercept? ____________

Converting linear Converting linear equations into Slope-equations into Slope-

Intercept FormIntercept Form

Converting linear Converting linear equations into Slope-equations into Slope-

Intercept FormIntercept Form

4 Warm-UP Examples4 Warm-UP Examples4 Warm-UP Examples4 Warm-UP Examples

Slope intercept form is:

y = mx + b

Our main goal is to get the y alone on one side of the equation

Example 1 - convert into Slope-Intercept Form

Example 1 - convert into Slope-Intercept Form

2 4 2y x 2 2

2 4 2y x 2 2 2

(divide both sides by 2 to get y alone)

2 4 2y x

(now simplify all fractions)2 1

2 1y x What is the slope? _____ What is the y-intercept? ______

Example 2 – Convert to Slope-Intercept Form

-3y = -9x – 12Step 1: divide both sides by -3 to get y alone

Step 2: Simplify all fractions

Step 3: Write your equation in y = mx + b

What is the slope? ____________

What is the y-intercept? ____________

*** Check Your Answer ***

-3y = -9x – 12 (divide both sides by -3 to get y alone)

(now simplify all fractions)

y = 3x + 4

-3 -3

-3y = -9x – 12-3 -3 -3

Slope = 3

Intercept = 4

Wow, you’re good at this!!

Example 3: Convert to Slope-Intercept Form

21x – 7y =14 (subtract both sides by 21x)

-7y = -21x + 14(now divide both sides by -7)

y = 3x – 2

(simplify all fractions)

21 -21xx

7 - 7 -7

What is the slope? _________

What is the y-intercept? ________

2y + 26 = -6x

Step 1: Subtract both sides by 26

Step 2: Divide both sides by 2 to get y by itself

Step 3: Simplify all fractions

Example 4: Convert to Slope-Intercept Form

What is the slope? ____________

What is the y-intercept? ____________

2y + 26 = -6x(subtract both sides by 26)

2y = -6x – 26(now divide both sides by 2

y = -3x – 13

(simplify all fractions)

You are a math wizard!

*** Check Your Answer ***

26 -26

2 2 2

Families of Linear Graphs

• http://www.glencoe.com/sites/texas/student/mathematics/assets/animation/algebra1/ALG1CIM4-3.swf

1 2 3 4 5

1

2

3

4

5

-1

-2

-3

-4

-5

-1-2-3-4-5 0

Step 2: Look at the Step 2: Look at the y-intercepty-intercept and and plot plot where the graph crosses the y-axis.where the graph crosses the y-axis.

Step 3: Use the Step 3: Use the slopeslope (rise/run) to determine (rise/run) to determine the next point and the next point and plot.plot. Slope = 2/3 = Slope = 2/3 = 22//33Step 4: Draw a line Step 4: Draw a line through both points. through both points. Be sure to extend the Be sure to extend the line and put arrows at line and put arrows at both ends. (Use a both ends. (Use a ruler!)ruler!)

y = 2/3x + 2 y

x

Step 5: Label your lineStep 5: Label your line

Step 1: Solve for yStep 1: Solve for y y = 2/3x + 2

1 2 3 4 5

1

2

3

4

5

-1

-2

-3

-4

-5

-1-2-3-4-5 0

Step 2: Look at the Step 2: Look at the y-intercepty-intercept and and plot plot where the graph crosses the y-axis.where the graph crosses the y-axis.

Step 3: Use the Step 3: Use the slopeslope (rise/run) to determine (rise/run) to determine the next point and the next point and plot.plot. Slope = 2 = Slope = 2 = 22//11Step 4: Draw a line Step 4: Draw a line through both points. through both points. Be sure to extend the Be sure to extend the line and put arrows at line and put arrows at both ends. (Use a both ends. (Use a ruler!)ruler!)

y = 2x + 1

x

y

Step 5: Label your lineStep 5: Label your line

Step 1: Solve for yStep 1: Solve for y

1 2 3 4 5

1

2

3

4

5

-1

-2

-3

-4

-5

-1-2-3-4-5 0

Step 2: Look at the Step 2: Look at the y-intercepty-intercept and and plot plot where the graph crosses the y-axis.where the graph crosses the y-axis.

Step 3: Use the Step 3: Use the slopeslope (rise/run) to determine (rise/run) to determine the next point and the next point and plot.plot. Slope = -1 = -Slope = -1 = -11//11Step 4: Draw a line Step 4: Draw a line through both points. through both points. Be sure to extend the Be sure to extend the line and put arrows at line and put arrows at both ends. (Use a both ends. (Use a ruler!)ruler!)

y = -x – 2

y

x

Step 5: Label your lineStep 5: Label your line

Step 1: Solve for yStep 1: Solve for y

Write the equation of the line, in slope-intercept form, that passes through (3, 5) and (5, 9)

m = (y2-y1)/(x2-x1)Step 1: Find the slopem = (9-5)/(5-3) = 4/2 = 2

Step 2: Plug in either coordinate into y = mx + b and solve for b

Step 3: Write the equation of the line by substituting the values you computed for m (step 1) and b (step 2) in y = mx + b

y = 2x – 1

(3, 5) (5, 9)y = mx + b y = mx+b

5 = 2(3) + b OR 9 = 2(5) + b5 = 6 + b 9 = 10 + b-1 = b -1 = b

Besides (3, 5) and (5, 9), what’s another point on this line? Hint: b=-1(0, -1)

Ex1:Write the equation of the line, in slope-intercept form, that passes through (3, 5) and (5, 9)

m = (y2-y1)/(x2-x1)Step 1: Find the slopem = (9-5)/(5-3) = 4/2 = 2

Step 2: Plug in either coordinate into y = mx + b and solve for b

Step 3: Write the equation of the line by substituting the values you computed for m (step 1) and b (step 2) in y = mx + b

y = 2x – 1

(3, 5) (5, 9)y = mx + b y = mx+b

5 = 2(3) + b OR 9 = 2(5) + b5 = 6 + b 9 = 10 + b-1 = b -1 = b

SWBAT… Write equations in slope-intercept form Tues, 1/4

Agenda1. WU (15 min)2. Review hw#5 (15 min)3. Quiz (15 min)

WARM-UP: Write the slope-intercept form of an

equation of the line that satisfies each condition:

1.) Has slope 3 and y-intercept -52.) Passes through (5, -7) and has a slope of 33.) Passes through (6, -3) and (12, -3)4.) Has an x-intercept of -2 and a y-intercept of

4 (Hint: write the two points)

2 problems