Beginning Algebra, 11th Edition

Identifying Slopes and y-Intercepts

Identify the slope and y-intercept of the line with each equation.

(a)

Slope y-intercept

(b) can be written as

Slope y-intercept

(c) can be written as

Slope y-intercept

(d) can be written as

Slope y-intercept

NOW TRY

A0, - 34 B

y= 4 x- 43 y=^14 x+ A- (^43) B.
1 0, 0 2

y= 6 x y= 6 x+ 0.

1 0, - 82

y=x- 8 y= 1 x+ 1 - 82.

1 0, 1 2

y= - 4 x+ 1

EXAMPLE 1

3.4 Writing and Graphing Equations of Lines

Remember: The intercept given by slope-intercept form is the y-intercept.

OBJECTIVES

Writing and Graphing Equations of Lines

3.4

1 Use the slope-

intercept form of

the equation of

a line.

2 Graph a line by

using its slope and

a point on the line.

3 Write an equation

of a line by using its

slope and any point

on the line.

4 Write an equation of

a line by using two

points on the line.

5 Write an equation

of a line that fits a

data set.

OBJECTIVE 1 Use the slope-intercept form of the equation of a line.In

Section 3.3,we found the slope (steepness) of a line by solving the equation of the

line for y. In that form, the slope is the coefficient of x. For example, the slope of the

line with equation is 2. What does the number 3 represent?

To find out, suppose a line has slope mand y-intercept. We can find an equa-

tion of this line by choosing another point on the line, as shown in FIGURE 29.

Then we use the slope formula.

y= mx+ b

mx+ b= y

mx= y- b

m=

y-b

x

m=

y-b

x- 0

1 x, y 2

1 0, b 2

y= 2 x+ 3

Change in y-values

Change in x-values

Subtract in the

denominator.

Multiply by x.

Add b.

Rewrite.

This result is the slope-intercept formof the equation of a line, because both the slope

and the y-intercept of the line can be read directly from the equation. For the line with

equation y= 2 x+ 3 , the number 3 gives the y-intercept 1 0, 32.

Slope-Intercept Form

The slope-intercept formof the equation of a line with slope mand y-intercept

is

Slope 1 0, b 2 is the y-intercept.

ymxb.

1 0, b 2

NOW TRY
EXERCISE 1
Identify the slope and
y-intercept of the line with
each equation.

(a)

(b)y=-

x

3

+

7

3

y=-

3

5

x- 9

NOW TRY ANSWERS

1. (a)slope: y-intercept:

(b)slope: - 31 ;y-intercept: A0,^73 B

• 35 ; 1 0, - 92

x

y

0

Slope

is

m.

(x, y)

(0, b)

FIGURE 29