# 5.1 write linear equations in slope-intercept .write linear equations in slope-intercept form goal     Post on 05-Jun-2018

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Write Linear Equations inSlope-Intercept FormGoal p Write equations of lines.

5.1

Write an equation of the line with a slope of 24 and a y-intercept of 6.

Solutiony 5 mx 1 b Write slope-intercept form.

y 5 x 1 Substitute for m and for b.

Example 1 Use slope and y-intercept to write an equation

Checkpoint Write an equation of the line with the given slope and y-intercept.

1. Slope is 8; 2. Slope is 2 } 3 ;

y-intercept is 25. y-intercept is 22.

3. Slope is 23; 4. Slope is 2 5 } 2 ;

y-intercept is 7. y-intercept is 9.

Use the slope-intercept form (y 5 mx 1 b) to write an equation of a line if slope and y-intercept are given.

Write Linear Equations inSlope-Intercept FormGoal p Write equations of lines.

5.1

Write an equation of the line with a slope of 24 and a y-intercept of 6.

Solutiony 5 mx 1 b Write slope-intercept form.

y 5 24 x 1 6 Substitute 24 for m and 6 for b.

Example 1 Use slope and y-intercept to write an equation

Checkpoint Write an equation of the line with the given slope and y-intercept.

1. Slope is 8; 2. Slope is 2 } 3 ;

y-intercept is 25. y-intercept is 22.

y 5 8x 1 (25) y 5 2 } 3 x 1 (22)

3. Slope is 23; 4. Slope is 2 5 } 2 ;

y-intercept is 7. y-intercept is 9.

y 5 23x 1 7 y 5 2 5 } 2 x 1 9

Use the slope-intercept form (y 5 mx 1 b) to write an equation of a line if slope and y-intercept are given.

Write an equation of the line shown.

SolutionStep 1 Calculate the slope.

x

y

1

3

12121

23

23 3

(3, 22)

(0, 4)

m 5 y2 2 y1 } x2 2 x1

5 2

2

5 5

Step 2 Write an equation of the line. The line crosses the y-axis at . So, the y-intercept is .

y 5 mx 1 b Write slope-intercept form.

y 5 x 1 Substitute for m and for b.

Example 2 Write an equation of a line given two points

You can write an equation of a line if you know the y-intercept and any other point on the line.

5. Write an equation of the line shown.

x

y1

12121

23

25

3 5

(5, 23)

(0, 26)

Checkpoint Complete the following exercise.

Write an equation of the line shown.

SolutionStep 1 Calculate the slope.

x

y

1

3

12121

23

23 3

(3, 22)

(0, 4)

m 5 y2 2 y1 } x2 2 x1

5 3

22

0

4

2

2

5 3

26 5 22

Step 2 Write an equation of the line. The line crosses the y-axis at (0, 4) . So, the y-intercept is 4 .

y 5 mx 1 b Write slope-intercept form.

y 5 22 x 1 4 Substitute 22 for m and 4 for b.

Example 2 Write an equation of a line given two points

You can write an equation of a line if you know the y-intercept and any other point on the line.

5. Write an equation of the line shown.

y 5 3 } 5 x 2 6

x

y1

12121

23

25

3 5

(5, 23)

(0, 26)

Checkpoint Complete the following exercise.

Write an equation for the linear function f with the values f(0) 5 4 and f(2) 5 12.

Solution

Step 1 Write f(0) 5 4 as and f(2) 5 12 as .

Step 2 Calculate the slope of the line that passes through and .

m 5 y2 2 y1 } x2 2 x1

5 2

2

5

5

Step 3 Write an equation of the line. The line crosses the y-axis at (0, ). So, the y-intercept is .

y 5 mx 1 b Write slope-intercept form.

y 5 Substitute for m and for b.

The function is .

Example 3 Write a linear function

Homework

6. Write an equation for the linear function with the values f(0) 5 3 and f(3) 5 15.

Checkpoint Complete the following exercise.

Write an equation for the linear function f with the values f(0) 5 4 and f(2) 5 12.

Solution

Step 1 Write f(0) 5 4 as (0, 4) and f(2) 5 12 as (2, 12).

Step 2 Calculate the slope of the line that passes through (0, 4) and (2, 12).

m 5 y2 2 y1 } x2 2 x1

5 2

12

0

4

2

2

5 2

8

5 4

Step 3 Write an equation of the line. The line crosses the y-axis at (0, 4 ). So, the y-intercept is 4 .

y 5 mx 1 b Write slope-intercept form.

y 5 4x 1 4 Substitute 4 for m and 4 for b.

The function is f (x) 5 4x 1 4.

Example 3 Write a linear function

Homework

6. Write an equation for the linear function with the values f(0) 5 3 and f(3) 5 15.

y 5 4x 1 3

Checkpoint Complete the following exercise.

• 5.2 Use Linear Equations inSlope-Intercept FormGoal p Write an equation of a line using points

on the line.

WRITING AN EQUATION OF A LINE IN SLOPE-INTERCEPT FORM

Step 1 Identify the slope . You can use the to calculate the slope if you know

two points on the line.

Step 2 Find the . You can substitute the and the of a point (x, y) on the line into y 5 mx 1 b. Then solve for .

Step 3 Write an equation using .

Write an equation of the line that passes through the point (1, 2) and has a slope of 3.

Solution

Step 1 Identify the slope. The slope is .

Step 2 Find the y-intercept. Substitute the slope and the coordinates of the given point into y 5 mx 1 b. Solve for b.

y 5 mx 1 b Write slope-intercept form.

5 ( ) 1 b Substitute for m, for x, and for y.

5 b Solve for .

Step 3 Write an equation of the line.

y 5 mx 1 b Write slope-intercept form.

y 5 Substitute for m and for b.

Example 1 Write an equation given the slope and a point

Be careful not to mix up the x- and y-values when you substitute.

• 5.2 Use Linear Equations inSlope-Intercept FormGoal p Write an equation of a line using points

on the line.

WRITING AN EQUATION OF A LINE IN SLOPE-INTERCEPT FORM

Step 1 Identify the slope m . You can use the slope formula to calculate the slope if you know two points on the line.

Step 2 Find the y-intercept . You can substitute the slope and the coordinates of a point (x, y) on the line into y 5 mx 1 b. Then solve for b .

Step 3 Write an equation using y 5 mx 1 b .

Write an equation of the line that passes through the point (1, 2) and has a slope of 3.

Solution

Step 1 Identify the slope. The slope is 3 .

Step 2 Find the y-intercept. Substitute the slope and the coordinates of the given point into y 5 mx 1 b. Solve for b.

y 5 mx 1 b Write slope-intercept form.

2 5 3 ( 1 ) 1 b Substitute 3 for m, 1 for x, and 2 for y.

21 5 b Solve for b .

Step 3 Write an equation of the line.

y 5 mx 1 b Write slope-intercept form.

y 5 3x 2 1 Substitute 3 for m and 21 for b.

Example 1 Write an equation given the slope and a point

Be careful not to mix up the x- and y-values when you substitute.

1. Write an equation of the line that passes through the point (2, 2) and has a slope of 4.

Checkpoint Complete the following exercise.

Write an equation of the line that passes through (2, 23) and (22, 1).

SolutionStep 1 Calculate the slope.

m 5 y2 2 y1 } x2 2 x1

5 2

2

5 5

Step 2 Find the y-intercept. Use the slope and the point (2, 23).

y 5 mx 1 b Write slope-intercept form.

23 5 ( ) 1 b Substitute for m, for x, and

for y.

5 b Solve for b.

Step 3 Write an equation of the line.

y 5 mx 1 b Write slope-intercept form.

y 5 Substitute for m and for b.

Example 2 Write an equation given two points

You can also find the y-intercept using the coordinates of the other given point.

1. Write an equation of the line that passes through the point (2, 2) and has a slope of 4.

y 5 4x 2 6

Checkpoint Complete the following exercise.

Write an equation of the line that passes through (2, 23) and (22, 1).

SolutionStep 1 Calculate the slope.

m 5 y2 2 y1 } x2 2 x1

5 22

1

2

(23)

2

2

5 24

4 5 21

Step 2 Find the y-intercept. Use the slope and the point (2, 23).

y 5 mx 1 b Write slope-intercept form.

23 5 21 ( 2 ) 1 b Substitute 21 for m, 2 for x, and 23 for y.

21 5 b Solve for b.

Step 3 Write an equation of the line.

y 5 mx 1 b Write slope-intercept form.

y 5 2x 2 1 Substitute 21 for m and 21 for b.

Example 2 Write an equation given two points

You c

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