Intermediate Algebra (11th edition)

Solve each equation for y. See Section 2.2.

101. 
     
     
     
     102. 
          
          
          
          103. 
               
          
          
          
          
     
     
     
     

Write each equation in the form See Section 2.1.

104. 105.y- 1 - 12 =-

1

2

y- 1 - 22 = 3 x- 1 - 224

3

2

1 x- 52

Ax+By=C.

3 x+ 2 y= 8 4 x+ 3 y= 0 y- 2 = 41 x+ 32

PREVIEW EXERCISES

4.1 Systems of Linear Equations in Two Variables

OBJECTIVES

Linear Equations in Two Variables

3.3

1 Write an equation

of a line, given

its slope and

y-intercept.

2 Graph a line, using

its slope and

y-intercept.

3 Write an equation

of a line, given its

slope and a point

on the line.

4 Write equations

of horizontal and

vertical lines.

5 Write an equation

of a line, given two

points on the line.

6 Write an equation

of a line parallel or

perpendicular to a

given line.

7 Write an equation

of a line that

models real data.

OBJECTIVE 1 Write an equation of a line, given its slope and y-intercept.

In Section 3.2,we found the slope of a line from its equation by solving the equation

for y. For example, we found that the slope of the line with equation

is 4 , the coefficient of x. What does the number 8 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 inFIGURE 25, and

using the slope formula.

Multiply by x.

Add b.

Rewrite.

This last equation is called the slope-intercept formof the equation of a line, because

we can identify the slope mand y-intercept at a glance. Thus, in the line with

equation y= 4 x+ 8 ,the number 8 indicates that the y-intercept is 1 0, 82.

1 0, b 2

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= 4 x+ 8

x

y

0

Slope

is

m.

(x, y)

(0, b)

FIGURE 25

Slope-Intercept Form

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

is

Slope y-intercept is 1 0, b 2.

ymxb.

1 0, b 2

Writing an Equation of a Line

Write an equation of the line with slope and y-intercept

Here, and Substitute these values into the slope-intercept form.

Slope-intercept form

y = - m=- 54 ;b=- 2 NOW TRY

4

5

x- 2

y= m x+b

m=- b=-2.

4

5

- 1 0, - 22.

4

5

EXAMPLE 1

NOW TRY
EXERCISE 1
Write an equation of the
line with slope and

y-intercept.

NOW TRY ANSWER

1. y=^23 x+ 1

1 0, 1 2

2

3