Section 3.5Slope-Intercept Form

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

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

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

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.

EXAMPLE 2

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

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.

EXAMPLE 4

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

EXAMPLE 4

Objective 5: Recognize Parallel and Perpendicular Lines The slope–intercept form enables us to

quickly identify parallel and perpendicular lines.

EXAMPLE 6 Are the graphs of y = −5x + 6 and x − 5y = −10

parallel, perpendicular, or neither?

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.

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.