Chapter 2Section 4

Write an equation in slope-intercept form for the line

that has a slope of and passes through (5, –2).

Slope-intercept form

Simplify.

Add 3 to each side.

Answer: The y-intercept is 1. So, the equation in

slope-intercept form is

Write an equation in slope-intercept form for the line

that has a slope of and passes through (–3, –1).

Answer:

Multiple-Choice Test Item

What is an equation of the line through (2, –3) and (–3, 7)?

A B

C D

Read the Test ItemYou are given the coordinates of two points on the line. Notice that the answer choices are in slope-intercept form.

Solve the Test ItemFirst, find the slope of the line.

Slope formula

Simplify.

The slope is –2. That eliminates choices B and C.

Then use the point-slope formula to find an equation.

Point-slope form

you can use eitherpoint for .

Distributive Property

Answer: D

Subtract 3 from each side.

Answer: C

Multiple-Choice Test Item

What is an equation of the line through (2, 5) and (–1, 3)?

A C

B D

Sales As a part-time salesperson, Jean Stock is paid a daily salary plus commission. When her sales are $100, she makes $58. When her sales are $300, she makes $78.Write a linear equation to model this situation.

Let x be her sales and let y be the amount of money she makes. Use the points (100, 58) and (300, 78) to

make a graph to represent the situation.

Slope formula

Simplify.

Now use the slope and either of the given points with the point-slope form to write the equation.

Point-slope form

Distributive Property

Add 58 to each side.

Answer: The slope-intercept form of the equation is

The y-intercept of the line is 48. The y-intercept represents the money Jean would make if she had no sales. Thus, $48 is her daily salary.

Answer: Ms. Stock’s daily salary is $48, and she makes a 10% commission.

What are Ms. Stock’s daily salary and commission rate?

The slope of the line is 0.1. Since the

slope is the coefficient of x, which is

her sales, she makes 10% commission.

How much would Jean make in a day if her sales were $500?

Find the value of y when

Use the equation you found in Example 3a.

Replace x with 500.

Simplify.

Answer: She would make $98 if her sales were $500.

Sales The student council is selling coupon books to raise money for the Humane Society. If the group sells 200 books, they will receive $150 dollars. If they sell 500 books, they will make $375.

a. Write a linear equation to model this situation.

b. Find the percentage of the proceeds that the studentcouncil receives.

c. If they sold 1000 books, how much money would they receive to donate to the Humane Society?

Answer:

Answer: 75%

Answer: $750

Write an equation for the line that passes through

(3, –2) and is perpendicular to the line whoseequation is

The slope of the given line is –5. Since the slopes of

perpendicular lines are opposite reciprocals, the slope

of the perpendicular line is

Use the point-slope form and the ordered pair (3, –2) to write the equation.

Point-slope form

Distributive Property

Subtract 2 from each side.

Answer: An equation of the line is

Write an equation for the line that passes through

(3, 5) and is perpendicular to the line whoseequation is

Answer: