Intermediate Algebra (11th edition)

Writing Equations of Horizontal and Vertical Lines

Write an equation of the line passing through the point

that satisfies the given condition.

(a)Slope 0

Since the slope is 0, this is a horizontal line. A hori-

zontal line through the point has equation

Here the y-coordinate is 3, so the equation is

(b)Undefined slope

This is a vertical line, since the slope is undefined. A

vertical line through the point has equation

Here the x-coordinate is so the equation is

Both lines are graphed in FIGURE 29.

- 3, x=-3.

1 a, b 2 x=a.

y= 3.

1 a, b 2 y=b.

1 - 3, 3 2

EXAMPLE 4

164 CHAPTER 3 Graphs, Linear Equations, and Functions

Equations of Horizontal and Vertical Lines

The horizontal line through the point has equation

The vertical line through the point 1 a, b 2 has equation xa.

1 a, b 2 yb.

x

y

(−3, 3)

y = 3

x = –3

0

–3

3

FIGURE 29

NOW TRY

OBJECTIVE 5 Write an equation of a line, given two points on the line.

InSection 3.1,we defined standard formfor a linear equation as

Standard form

where A,B, and Care real numbers and Aand Bare not both 0. (In most cases, A,B,

and Care rational numbers.) For consistency in this book, we give answers so that A,

B, and Care integers with greatest common factor 1, and For example, the

equation in Example 3is written in standard form as follows.

Equation from Example 3

Subtract xand add 15.

Standard form Multiply by.

NOTE The definition of “standard form” is not standard among texts. A linear equa-

tion can be written in many different, equally correct ways. For example, the equa-

tion can be written as

and

We prefer the standard form over any multiples of each side, such as

(To write in this preferred form, divide each side by 2.)

Writing an Equation of a Line, Given Two Points

Write an equation of the line passing through the points and Give

the final answer in standard form.

First find the slope by the slope formula.

m=

- 7 - 3

5 - 1 - 42

= -

10

9

1 - 4, 3 2 1 5, - 72.

EXAMPLE 5

4 x+ 6 y= 16. 4 x+ 6 y= 16

2 x+ 3 y= 8

x+ 4 x+ 6 y= 16.

3

2

2 x= 8 - 3 y, 3 y= 8 - 2 x, y=4,

2 x+ 3 y= 8

x- 3 y=- 17 - 1

- x+ 3 y= 17

3 y- 15 =x+ 2 1 * 2

AÚ0.

AxByC,

NOW TRY
EXERCISE 4
Write an equation of the line
passing through the point
that satisfies the
given condition.

(a)Undefined slope

(b)Slope 0

1 4, - 42

NOW TRY ANSWERS

4. (a)x= 4 (b)y=- 4