1. Section 3.5 Slope-Intercept Form

2. Objectives Use slope–intercept form to identify the slope and y-intercept of a line Write a linear equation in slope–intercept form Write an equation of a line given its slope and y-intercept Use the slope and y-intercept to graph a linear equation Recognize parallel and perpendicular lines Use slope–intercept form to write an equation to model data

3. Objective 1: Use Slope–Intercept Form to Identify the Slope and y-Intercept of a Line

4. EXAMPLE 1 Find the slope and y-intercept of the line with the given equation. a. 8x + y = 9 b. x + 4y = 16 c. −9x − 3y = 11

5. Objective 3: Write an Equation of a Line Given Its Slope and y-Intercept If we are given the slope and y-intercept of a line, we can write an equation of the line by substituting for m and b in the slope–intercept form.

6. EXAMPLE 2 Write an equation of the line with slope −1 and y-intercept (0, 9).

7. Objective 4: Use the Slope and y-Intercept to Graph a Linear Equation If we know the slope and y-intercept of a line, we can graph the line.

8. EXAMPLE 4 Use the slope and y-intercept to graph y = 5x − 4.

9. EXAMPLE 4

10. Objective 5: Recognize Parallel and Perpendicular Lines The slope–intercept form enables us to quickly identify parallel and perpendicular lines.

11. EXAMPLE 6 Are the graphs of y = −5x + 6 and x − 5y = −10 parallel, perpendicular, or neither?

12. Objective 6: Use Slope–Intercept Form to Write an Equation to Model Data To make the equation more descriptive, we replace x and y in y = mx + b with two other variables.

13. EXAMPLE 7 Group Discounts To promote group sales for an Alaskan cruise, a travel agency reduces the regular ticket price of $4,500 by $5 for each person traveling in the group. a. Write a linear equation that determines the per-person cost c of the cruise, if p people travel together. b. Use the equation to determine the per-person cost if 55 teachers travel together.