Slope-Intercept Form Unit 3 Module 11 Lesson 2 Holt Algebra 1 Holt McDougal Algebra 1

Warm Up Find 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 –1 –2 y = 3x + 11

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

Additional Example 1: Graphing by Using Slope and y-intercept Graph the line given the slope and y-intercept. ; y intercept = 4 Slope =-

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.

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

Additional Example 2B: Writing Linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form. slope = –9; y-intercept =

Additional Example 2C: Writing Linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form.

Additional Example 2D: Writing linear Equations in Slope-Intercept Form Write the equation that describes the line in slope-intercept form. slope = 2; (3, 4) is on the line.

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.

Additional Example 3B: Using Slope-Intercept Form to Graph Write the equation in slope-intercept form. Then graph the line described by the equation. 2y + 3x = 6

Check It Out! Example 3c Write the equation in slope-intercept form. Then graph the line described by the equation. y = –4

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.

Additional Example 4: Application 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. a. Write an equation that represents the cost as a function of the number of hours. b. Identify the slope and y-intercept and describe their meanings. c. Find the cost if the organizer works 12 hrs.

Point-Slope Form Unit 3 Module 11 Lesson 3 Holt Algebra 1 Holt McDougal Algebra 1

Objectives Graph a line and write a linear equation using point-slope form. Write a linear equation given two points.

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)

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)

Additional Example 2A: Using Point-Slope Form to Graph Graph the line described by the equation. y – 1 = 2(x – 3)

Additional Example 2B: Using Point-Slope Form to Graph Graph the line described by the equation. (2,7) (-2,4)

Additional Example 3A: Writing Linear Equations in Slope-Intercept Form Write the equation that describes each line in slope-intercept form. Slope = 3, (–1, 4) is on the line.

Additional Example 3B Continued Write an equation in slope-intercept form for the line through the two points. (2, –3) and (4, 1)

Additional Example 3C: Writing Linear Equations in Slope-Intercept Form Write the equation that describes the line in 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).

Additional 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.

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

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.

Homework Pg. 284-285 (14-26, 32-36 even) Pg. 291-293 (18 – 38 even)