Over Lesson 8–7

A. A

B. B

C. C

D. D

Find the slope and y-intercept for the graph of y = x + 5.

Find the slope and y-intercept for

You have already graphed linear equations using the slope and y-intercept. (Lesson 8–7)

• Write equations given the slope and y-intercept, a graph, a table, or two points.

• Use linear equations to solve problems.

• point-slope form An equation of the form y – y1 = m (x – x1), where m is the slope and (x1, y1) is a given point on a nonvertical line

Write the Equation of a Line in Slope-Intercept Form

y = mx + b Slope-intercept form

Answer:

A. Write an equation in slope-intercept form for the

line with slope and y-intercept 7.

Write the Equation of a Line in Slope-Intercept Form

B. Write an equation in slope-intercept form for the line graphed.

The y-intercept is –4. From (0, –4), you can go up one unit and to the right one unit to another point on the line. So, the slope is 1.

Write the Equation of a Line in Slope-Intercept Form

y = mx + b Slope-intercept form

Answer: y = x – 4

y = 1x + (–4) Replace m with 1 and b with –4.

y = x – 4 Simplify.

A. A

B. B

C. C

D. D

A. y = –3x + 5

B. 3x + y = –5

C. y = –5x – 3

D. y = –3x – 5

A. Write an equation in slope-intercept form for theline with slope –3 and y-intercept –5.

A. A

B. B

C. C

D. D

B. Write an equation in slope-intercept form for the line graphed.

A.

B.

C.

D.

Write an Equation Given Two Points

Write an equation for the line that passes through the points (7, 0) and (6, 3).

Step 1 Find the slope m.

Definition of slope

(x1, y1) = (7, 0)

(x2, y2) = (6, 3)

Simplify.

Write an Equation Given Two Points

Step 2 Use the slope and the coordinates of eitherpoint to write the equation in point-slope form.

y – y1 = m(x – x1) Point-slope form

y – 0 = –3(x – 7) Replace (x1, y1) with (7, 0) and m with –3.

y = –3x + 21 Simplify.

Answer: y = –3x + 21

A. A

B. B

C. C

D. D

Write an equation for the line that passes through (4, –2) and (–2, –14).

A. y = –8x + 30

B.

C. y = 2x + 6

D. y = 2x – 10

Write an Equation From a Table

Write an equation of the line in point-slope form that passes through the points shown in the table.

Step 1 Find the slope m. Use the coordinates of any two points.

Definition of slope

(x1, y1) = (–2, 16)

(x2, y2) = (–1, 10)

Simplify.

Write an Equation From a Table

Step 2 To write the equation, use the slope and thecoordinates of any point.

y – y1 = m(x – x1) Point-slope form

y – (–2) = –6(x – 1) Replace (x1, y1) with (1, –2) and m with –6.

y + 2 = –6(x – 1) Simplify.

Answer: The equation is y + 2 = –6(x – 1) or y = –6x + 4.

A. A

B. B

C. C

D. D

Use the table of values to write an equation in slope-intercept form.

A.

B.

C.

D.

Write an Equation to Make a Prediction

BUSINESS The number of customers living within 5 miles of a restaurant is 150. The number of customers decreases by 30 for every 5 miles beyond the original 5-mile radius. Estimate the number of customers who live between 15 and 20 miles away.

Understand You know the rate of change of number of customers to each 5-mile radius (slope) and the number of customers in the area immediately surrounding the restaurant (y-intercept). Make a table of ordered pairs.

Write an Equation to Make a Prediction

Plan Write an equation to show the relationship between the distance x and the number of customers y. Then, substitute the distance of 20 miles into the equation to find the number of customers.

SolveFind the slope m.

decrease of 30 customers

increase of 5 miles

Write an Equation to Make a Prediction

Find the y-intercept b.

When the distance is 0 miles, the number of customers is 150. So, the y-intercept is 150.

(x, y) = (distance, customers)

= (0, b)

Write the equation.

y = –6x + 150

Write an Equation to Make a Prediction

Substitute the distance of 20 miles.

y = –6x + 150 Write the equation.

y = –6(20) + 150 Replace x with 20.

y = 30 Simplify.

Answer: At a distance of 20 miles, the number of customers is 30.

A. A

B. B

C. C

D. D

A. 112 people

B. 300 people

C. 312 people

D. 412 people

WEATHER Attendance at an outdoor sporting event is affected by the temperature outside. When the outside temperature is 0°F, the attendance is 12 people. For every increase in temperature of 20 degrees, the attendance increases by 100 people. Predict the attendance if the temperature is 60°F.