Intermediate Algebra (11th edition)

(b)To be perpendicular to the line a line must have a slope that is the

negative reciprocal of which is We use and slope in the point-

slope form to find the equation of the perpendicular line shown in FIGURE 32.

Definition of subtraction

Distributive property

y= Add. 6 =^122

3

2

x+

21

2

y- 6 =

3

2

x+

9

2

y- 6 =

3

2

1 x+ 32

y - 6 = y 1 =6,m=^32 ,x 1 =- 3

3

2

3 x- 1 - 324

3

1 - 3, 6 (^22)
3

- 2.

2

3 ,

2 x+ 3 y= 6,

166 CHAPTER 3 Graphs, Linear Equations, and Functions

0

y

x

6

2

y = –^23 x + 2

–7 –3 3

(–3, 6)

y =^32 x +^21 2

FIGURE 32

NOW TRY

A summary of the various forms of linear equations follows.

Forms of Linear Equations

Equation Description When to Use

Slope-Intercept Form

Slope is m.

y-intercept is

Point-Slope Form

Slope is m.

Line passes through

Standard Form

(A, B, and Cintegers, )

Slope is.

x-intercept is.

y-intercept is.

Horizontal Line

Slope is 0.

y-intercept is

Vertical Line

Slope is undefined.

x-intercept is 1 a, 0 2.

xa

1 0, b 2.

yb

A0, CBB^1 BZ^02

ACA, 0B^1 AZ^02

• AB 1 BZ 02

AÚ 0

AxByC

1 x 1 , y 12.

yy 1 m 1 xx 12

1 0, b 2.

ymxb The slope and y-intercept can be

easily identified and used to quickly

graph the equation.

This form is ideal for finding the

equation of a line if the slope and

a point on the line or two points

on the line are known.

The x- and y-intercepts can be found

quickly and used to graph the

equation. The slope must be

calculated.

If the graph intersects only the

y-axis, then yis the only variable

in the equation.

If the graph intersects only the

x-axis, then xis the only variable

in the equation.

OBJECTIVE 7 Write an equation of a line that models real data.If a given

set of data changes at a fairly constant rate, the data may fit a linear pattern, where

the rate of change is the slope of the line.

Determining a Linear Equation to Describe Real Data

A local gasoline station is selling 89-octane gas for $3.20 per gal.

(a) Write an equation that describes the cost yto buy xgallons of gas.

The total cost is determined by the number of gallons we buy multiplied by the

price per gallon (in this case, $3.20). As the gas is pumped, two sets of numbers spin

by: the number of gallons pumped and the cost of that number of gallons.

EXAMPLE 7

NOW TRY
EXERCISE 6
Write an equation of the line
passing through the point
and

(a)parallel to the line
;

(b)perpendicular to the line
.

Give final answers in slope-
intercept form.

3 x- 5 y= 7

3 x- 5 y= 7

1 6, - 12

NOW TRY ANSWERS

6. (a)

(b)y=- 53 x+ 9

y=^35 x-^235