Holt Algebra 1

5-7 Point-Slope Form

Warm UpFind the slope of the line containing each pair of points.

1. (0, 2) and (3, 4) 2. (–2, 8) and (4, 2)

3. (3, 3) and (12, –15)

Write the following equations in slope-intercept form.

4. y – 5 = 3(x + 2)

5. 3x + 4y + 20 = 0

Holt Algebra 1

5-7 Point-Slope Form

Graph a line and write a linear equation using point-slope form.

Write a linear equation given two points.

Objectives

Holt Algebra 1

5-7 Point-Slope Form

In lesson 5-6 you saw that if you know the slope of a line and the y-intercept, you can graph the line. You can also graph a line if you know its slope and any point on the line.

Holt Algebra 1

5-7 Point-Slope Form

Example 1A: Using Slope and a Point to Graph

Graph the line with the given slope that contains the given point.

slope = 2; (3, 1)

Holt Algebra 1

5-7 Point-Slope Form

slope = ; (–2, 4)

Example 1B: Using Slope and a Point to Graph

Graph the line with the given slope that contains the given point.

Holt Algebra 1

5-7 Point-Slope Form

Example 1C: Using Slope and a Point to Graph

Graph the line with the given slope that contains the given point.

slope = 0; (4, –3)

Holt Algebra 1

5-7 Point-Slope Form

Check It Out! Example 1

Graph the line with slope –1 that contains (2, –2).

Holt Algebra 1

5-7 Point-Slope Form

If you know the slope and any point on the line, you can write an equation of the line by using the slope formula. For example, suppose a line has a slope of 3 and contains (2, 1). Let (x, y) be any other point on the line.

3(x – 2) = y – 1

y – 1 = 3(x – 2)

Slope formula

Substitute into the slope formula.

Multiply both sides by (x – 2).

Simplify.

Holt Algebra 1

5-7 Point-Slope Form

Holt Algebra 1

5-7 Point-Slope Form

Example 2: Writing Linear Equations in Point-Slope Form

Write an equation in point-slope form for the line with the given slope that contains the given point.A. B. C.

Holt Algebra 1

5-7 Point-Slope Form

Check It Out! Example 2

Write an equation in point-slope form for the line with the given slope that contains the given point.

a. b. slope = 0; (3, –4)

Holt Algebra 1

5-7 Point-Slope FormExample 3: Writing Linear Equations in Slope-Intercept

Form

Write an equation in slope-intercept form for the line with slope 3 that contains (–1, 4).

Step 1 Write the equation in point-slope form:

Step 2 Write the equation in slope-intercept form by solving for y.

Holt Algebra 1

5-7 Point-Slope Form

Check It Out! Example 3

Write an equation in slope-intercept form for

the line with slope that contains (–3, 1).

Add 1 to both sides.

Holt Algebra 1

5-7 Point-Slope Form

Check It Out! Example 3 Continued

Write an equation in slope-intercept form for

the line with slope that contains (–3, 1).

Holt Algebra 1

5-7 Point-Slope Form

Example 4A: Using Two Points to Write an Equation

Write an equation in slope-intercept form for the line through the two points.

(2, –3) and (4, 1)

Holt Algebra 1

5-7 Point-Slope Form

Example 4A Continued

Write an equation in slope-intercept form for the line through the two points.

(2, –3) and (4, 1)

Holt Algebra 1

5-7 Point-Slope Form

Example 4B: Using Two Points to Write an Equation

Write an equation in slope-intercept form for the line through the two points.

(0, 1) and (–2, 9)

Holt Algebra 1

5-7 Point-Slope Form

Example 4B Continued

Write an equation in slope-intercept form for the line through the two points.

(0, 1) and (–2, 9)

Holt Algebra 1

5-7 Point-Slope Form

Check It Out! Example 4a

Write an equation in slope-intercept form for the line through the two points.

(1, –2) and (3, 10)

Holt Algebra 1

5-7 Point-Slope Form

Check It Out! Example 4a Continued

Write an equation in slope-intercept form for the line through the two points.

(1, –2) and (3, 10)

Holt Algebra 1

5-7 Point-Slope Form

Check It Out! Example 4b

Write an equation in slope-intercept form for the line through the two points.

(6, 3) and (0, –1)

Holt Algebra 1

5-7 Point-Slope Form

Check It Out! Example 4b Continued

Write an equation in slope-intercept form for the line through the two points.

(6, 3) and (0, –1)

Holt Algebra 1

5-7 Point-Slope Form

Example 5: Problem-Solving Application

The cost to stain a deck is a linear function of the deck’s area. The cost to stain 100, 250, 400 square feet are shown in the table. Write an equation in slope-intercept form that represents the function. Then find the cost to stain a deck whose area is 75 square feet.

Holt Algebra 1

5-7 Point-Slope Form

Check It Out! Example 5

What if…? At a newspaper the costs to place an ad for one week are shown. Write an equation in slope-intercept form that represents this linear function. Then find the cost of an ad that is 21 lines long.

Holt Algebra 1

5-7 Point-Slope Form

Lesson Quiz: Part I

Write an equation in slope-intercept form for the line with the given slope that contains the given point.

1. Slope = –1; (0, 9)

2. Slope = ; (3, –6)

Write an equation in slope-intercept form for the line through the two points.

3. (–1, 7) and (2, 1)

4. (0, 4) and (–7, 2)

Holt Algebra 1

5-7 Point-Slope Form

Lesson Quiz: Part II

5. The cost to take a taxi from the airport is a linear function of the distance driven. The cost for 5, 10, and 20 miles are shown in the table. Write an equation in slope-intercept form that represents the function.