algebra i chapter 5 section 3 · web view3) state the slope intercept form equation for a line: 4)...

CC Math I Standards: Unit 5SLOPE-INTERCEPT FORM: Part 1

Warm Up Activity:1) Find slope of (3, 12) and (6, -6) 2) Find slope of (4, 8) and (-5, 8) 3) Find slope of (-5, 2) and (7, 6)

What is the Y – INTERCEPT of a line?The POINT where the line crosses the y – axis is called the y-intercept = (0, b)

Identify the y-intercept of each line Y-AXIS: vertical axis Follow the line until it reaches y- axis

o Draw Intercept pointo Find the coordinate of that point

Example: Line #1: Line #1 cross the y-axis at (0 , 5)

Line #2: Line #3:

Line #4: Line #5:

Line #6: Line #7:

What is Slope-Intercept Form?

Identify the Slope and Y-Intercept in each of the following equations:1) y = 3x + 5

2) y = 7 + 9x

3) -4x – 3 = y

4)

5) y = 112 + 87x

6) 0.4x – 2 = y

7)

8)

9)

10)

11) 6 – 7x = y

12) y = 23

Line #1

Line #2

Line #3

Line #5

Line #7

Line #6

Line #4

y

x

Write the Equation of a line given slope and y – intercept:1) b = 17/5 and m = 3

3) m = ¼ and (0, -6)

5) b = 5/7 and m = -3/7

2) Slope of 3 and y – intercept is 5.

4) Slope of -2 and (0, 4)

6) Y – intercept is -2 and slope is - ¼.

Write the Equation of a line in each graph: IDENTIFY the y-intercept (b) of the line and the slope (m) of the line WRITE y = mx + b equation by substituting m and b values.

1) Slope:

Y – Intercept:

Equation:

2) Slope:

Y – Intercept:

Equation:

3) Slope:

Y – Intercept:

Equation:

4) Slope:

Y – Intercept: Equation:

5) Slope:


6) Slope:


GRAPHING LINES BY HAND: How do you graph a line in slope intercept form?1) PLOT the y – intercept.2) From y – intercept perform SLOPE (RISE over RUN) to plot a second point.3) Draw a line between the two points.

1)

y-intercept =

Slope =

Rise =

Run =

2)

y-intercept =

Slope =

Rise =

Run =

3) y = 1 – 4xy-intercept =

Slope =

Rise =

Run =

4) y = 3x - 2

5)

y-intercept =

Slope =

Rise =

Run =

6)

y-intercept =

Slope =

Rise =

Run =

7)

y-intercept =

Slope =

Rise =

Run =

8)

1) Identify the SLOPE and Y-INTERCEPT in each equation:

1a. 1b.

1c. 1d.

1e. 1f.

2)Write the SLOPE-INTERCEPT FORM for each line:Line #1 Equation:Line #2 Equation:

Line #3 Equation:

LINE #1

LINE #3

LINE #2

HOW DO YOU DETERMINE IF A POINT IS ON A LINE? For each point (x, y), SUBSTITUTE the x-value and y-value into the equation. CHECK if both sides of the equation

o If EQUAL SIDES, then point IS on lineo If NOT EQUAL SIDES, the point IS NOT on line

Example: y = 3x – 4 Check: (1, -1) (2, 6) (-3, 13) (-4, -16) (5, 11)

PRACTICE PROBLEMS:1) Check: (1, 12), (-3, 21), (2, 11)

2) Check: (-2, -7), (3, 44), 6, 25)

3) Check: (8, 1), (4, 3), (-6, 2)

4) Check: (12, -16), (-4, 4), (4, 4)

5) Check: (3, -1) , (1, -5) , (0, 8)

6) Check: (6, 3), (-3, -1), (-9, -5)

REVIEW: Graph a line for each of the following for a given point and a slope.

1) point = (0, -2); m = 5/2 2) point = (2, 1) ; m = -3/2 3) point = (-3,4); m = -1

Based on graphs above, write equation of each line in SLOPE-INTERCEPT FORM:1) 2) 3)

How do we find the equation of a line without graphing?CASE #1: FIND THE Y-INTERCEPT of a line when you have the slope and any point.

What is the equation for slope-intercept form?

Example #1: Line that passes through (1, 5) and has a slope of 2.Step #1: SUBSTITUTE known values into slope- intercept form

Step #2: SOLVE for b.

Step #3: WRITE the equation with x and y as variables

Example #2: Line that passes through (2, -3) with slope of ½.Step #1 and 2:

Step #3: Equation

Find Equation in Slope-Intercept Form…Example 3: Line that passes through (1, -4) with a slope of –5/2.Step #1 and 2: Step #3: Equation

Example 4: Line that passes through (5, 5) with a slope of 1/3.

Example 5: Line that passes through (-9, 8) with a slope of -5/3.

Example 6: Line that passes through (-3, -7) and m = 4.

SPECIAL CASE: UNDEFINED SLOPE

1) Write an equation of a line that passes through (1, 3) with a slope of UNDEFINED.

2) Write an equation of a line with an undefined slope through the point (-2, 12).

3) Write an equation of a line has y-intercept of 5 with an undefined slope.

CLASSROOM WORK: Use a separate piece of paper,Write an equation of a line that passes through each point with the given slope.1) (-3, 3) and m = 1;

2) (0, 6) and slope = -

2; 3) (1, 6) and m = ½;

4) m = -3/5 and (4, -

3);

5) (5, -3) and slope = 3/2; 6) (4, -2) and m = 0;

CC Math I Standards: Unit 5Review of Last Week

1) State the SLOPE Formula:

2) Find the slope of the line for each pair of points:2a. (3, 4) and (5, 8)

2b. (-2, -9) and (-3, -6)

2c. (6, -4) and (8, -4)

2d. (2, 3) and (-5, -1)

2e. (7, 2) and (7, -2)

2f. (-5, 7) and (1, -2)

3) State the SLOPE INTERCEPT FORM Equation for a line:

4) For each graph, FIND the slope and y-intercept to write the equation of the line:

5) For the given point (x, y) and slope, m, find the SLOPE INTERCEPT FORM of line.

STEP by STEP Example: (4, 2) and slope = 3What do you know? Substitute and Solve Write Equation

y = 2

x = 4

m = 3

b = ??

y = mx + b

2 = 3*4 + b

2 = 12 + b

-10 = b

y = mx + b

y = 3x – 10

Keep x and y as variables.

5a. (0, 1) and slope = 1/3

5b. m = -2 and (-1, 3)

5c. (-5, -3) and

5d. (10, -3) and m = 0

5e. (9, 11) and

5f. slope = 4 and (0, -7)

5g. (14, 6) and

5h. (2, -4) and m = -1

5i. and (6, 7)


Find the SLOPE-INTERCEPT FORM of a line when given ANY two points on the line?

3 STEP PROCESS: Given two points (x1, y1) and (x2, y2) on a lineStep 1: FIND the SLOPE of line: (REDUCE FRACTIONS!!!!)

Step 2: PICK one point and the slope to FIND the Y-INTERCEPT.o (x1,y1) and mo Find the y-intercept (b) for y1 = m x1 + b (REDUCE FRACTIONS!!!!)

Step 3: WRITE the equation of the line in SLOPE-INTERCEPT FORM.o Use the m from Step 1 and b from Step 2o y = mx + b

STEP BY STEP: Find the Slope Intercept Form of the line through (5, 7) and (3, 1).

#1: SLOPE #2: Y-INTERCEPT #3: EQUATION(5, 7) and (3, 1). and (5, 7)

y = mx + b

-8 = b

y = mx + b

y = 3x – 8

Keep x and y as variables.

Example 1: Find the Slope Intercept Form of the line through (-3, 2) and (5, -14)

Example 2: Find the equation of the line that passes through (4, 7) and (8, 12).

Example 3: Find the equation of the line that passes through (0, 6) and (5, 0).

Example 4: Find the Slope Intercept Form of the line through (3, 4) and (-2, 4).

Example 5: Find the Slope Intercept Form of the line through (-1, 3) and (4, -1).

SPECIAL CASE: Find the equation of the line that passes through (-1, 3) and (-1, -8).

CLASSWORK PRACTICE: Use Separate paper as needed. Find the Slope Intercept Form of the line through each of points.

1. (3, -5) and (6, 4)

2. (-2, 20) and (2, 4)

3. (0, -3) and (2, 0)

4. (2, -4) and (2, 6)

5. (-4, -5) and (6, -1)

6. (3, -3) and (1, -3)

7. (6, 2) and (4, 4)

8. (4, 5) and (-3, -1)

9. (-2, -7) and (8, 8)


Find Slope Intercept Form of a Line when given a Linear Equation Y Coefficient of One Case

SIMPLIFY and MOVE “x terms” or “number terms” by addition or subtraction

For Problems #1 – 6: SOLVE for y, then IDENTIFY the Slope and Y-Intercept

1) 3x = 5 + y 2) y – 8 = 2x + 3 3)

4) 7 = 6x + y – 2 5) 5(7 – x) = y 6) y – 3x + 5 = 12

For Problems #7 – 12: Find Slope Intercept Form AND GRAPH the Line Identify the Slope and Y-Intercept

7) 1 = -3x + y

8) y + 7 = x + 3 9) 2(x – 2) = y

10)

11) -2x + y = 0

12)


Find Slope Intercept Form of a Line when given a Linear Equation Non-One Coefficients of y Case

Simplify both sides (if needed) Move “x terms” or constants by addition or subtraction to one side Divide all terms by the coefficient of y REDUCE All Fractions

Example 1: 3y + 6x = 10 Example 2: 10y – 5x = 8 Example 3: 8x – 4y = 12

Practice Problems: Solve for Slope Intercept Form and Identify the slope and y-intercept1) 9y – 3x = 18

2) 8x - 2y = 7

3) 14y – 35x = 63

4) x – 5y = 6

5) x + 5y = 8

6) 21 = 7y – 2x

7) 15 = -7x + 6y

8) 9 = 4y – x

9) 9x + 3y = 0

algebra i chapter 5 section 3 · web view3) state the slope intercept form equation for a line: 4)...

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