Holt McDougal Algebra 1

Slope-Intercept FormSlope-Intercept Form

Holt Algebra 1

Lesson 2Lesson 2

Module 11Module 11

Unit 3Unit 3

Holt McDougal Algebra 1

Holt McDougal Algebra 1

Slope-Intercept 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

–2

–1

y = 3x + 11

Holt McDougal Algebra 1

Slope-Intercept Form

Write a linear equation in slope-intercept form.Graph a line using slope-intercept form.

Objectives

Holt McDougal Algebra 1

Slope-Intercept Form

You have seen that you can graph a line if you know two points on the line. Another way is to use the slope of the line and the point that contains the y-intercept.

Holt McDougal Algebra 1

Slope-Intercept Form

Additional Example 1: Graphing by Using Slope and y-intercept

Graph the line given the slope and y-intercept.

; y intercept = 4Slope =-25

Holt McDougal Algebra 1

Slope-Intercept Form

Any linear equation can be written in slope-intercept form by solving for y and simplifying. In this form, you can immediately see the slope and y-intercept. Also, you can quickly graph a line when the equation is written in slope-intercept form.

Holt McDougal Algebra 1

Slope-Intercept Form

Additional Example 2A: Writing Linear Equations in Slope-Intercept Form

Write the equation that describes the line in slope-intercept form.

slope = ; y-intercept = 4

Holt McDougal Algebra 1

Slope-Intercept Form

slope = –9; y-intercept =

Additional Example 2B: Writing Linear Equations in Slope-Intercept Form

Write the equation that describes the line in slope-intercept form.

Holt McDougal Algebra 1

Slope-Intercept Form

Additional Example 2C: Writing Linear Equations in Slope-Intercept Form

Write the equation that describes the line in slope-intercept form.

Holt McDougal Algebra 1

Slope-Intercept Form

slope = 2; (3, 4) is on the line.

Additional Example 2D: Writing linear Equations in Slope-Intercept Form

Write the equation that describes the line in slope-intercept form.

Holt McDougal Algebra 1

Slope-Intercept Form

Check It Out! Example 2d

A line has a slope of 8 and (-3, 1) is on the line. Write the equation that describes this line in slope-intercept form.

Holt McDougal Algebra 1

Slope-Intercept FormAdditional Example 3B: Using Slope-Intercept Form to

GraphWrite the equation in slope-intercept form. Then graph the line described by the equation.

2y + 3x = 6

Holt McDougal Algebra 1

Slope-Intercept Form

Check It Out! Example 3c

y = –4

Write the equation in slope-intercept form. Then graph the line described by the equation.

Holt McDougal Algebra 1

Slope-Intercept Form

Additional Example 4: Application

A closet organizer charges a $100 initial consultation fee plus $30 per hour. The cost as a function of the number of hours worked is graphed below.

Holt McDougal Algebra 1

Slope-Intercept Form

Additional Example 4: Application

a. Write an equation that represents the cost as a function of the number of hours.

A closet organizer charges $100 initial consultation fee plus $30 per hour. The cost as a function of the number of hours worked is graphed below.

b. Identify the slope and y-intercept and describe their meanings.

c. Find the cost if the organizer works 12 hrs.

Holt McDougal Algebra 1

Slope-Intercept FormPoint-Slope Form

Holt Algebra 1

Lesson 3Lesson 3

Module 11Module 11

Unit 3Unit 3

Holt McDougal Algebra 1

Holt McDougal Algebra 1

Slope-Intercept Form

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

Write a linear equation given two points.

Objectives

Holt McDougal Algebra 1

Slope-Intercept Form

Holt McDougal Algebra 1

Slope-Intercept Form

Additional Example 1A: 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.

y – y1 = m (x – x1)

Holt McDougal Algebra 1

Slope-Intercept Form

Additional Example 1B: 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.

slope = –4; (0, 3)

Holt McDougal Algebra 1

Slope-Intercept Form

Additional Example 2A: Using Point-Slope Form to Graph

y – 1 = 2(x – 3)

Graph the line described by the equation.

Holt McDougal Algebra 1

Slope-Intercept Form

Graph the line described by the equation.

Additional Example 2B: Using Point-Slope Form to Graph

(-2,4)(2,7)

Holt McDougal Algebra 1

Slope-Intercept Form

Write the equation that describes each line in slope-intercept form.

Additional Example 3A: Writing Linear Equations in Slope-Intercept Form

Slope = 3, (–1, 4) is on the line.

Holt McDougal Algebra 1

Slope-Intercept Form

Additional Example 3B Continued

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

(2, –3) and (4, 1)

Holt McDougal Algebra 1

Slope-Intercept Form

Additional Example 3C: Writing Linear Equations in Slope-Intercept Form

Write the equation that describes the line in slope-intercept form.

Holt McDougal Algebra 1

Slope-Intercept Form

Check It Out! Example 3a Continued

Write an equation in slope-intercept form for

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

Holt McDougal Algebra 1

Slope-Intercept FormAdditional Example 4: Using Two Points Find Intercepts

Write an equation in slope-intercept form for the line through (10, –3) and (5, –2). Then find the intercepts.

Holt McDougal Algebra 1

Slope-Intercept Form

Write an equation in slope-intercept form for the line through the two points. Then find the intercepts.(2, 15) and (–4, –3)

Holt McDougal Algebra 1

Slope-Intercept 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 McDougal Algebra 1

Slope-Intercept Form

Homework

Pg. 284-285 (14-26, 32-36 even)

Pg. 291-293

(18 – 38 even)