Equations Of Lines In Slope-Intercept And Standard Form Worksheet (Page 4 of 9) in pdf

Equations Of Lines In Slope-Intercept And Standard Form Worksheet Page 4

184

(4–28)

Chapter 4 Linear Equations in Two Variables and Their Graphs

When using the slope to ﬁnd a second point on the line, be

C A U T I O N

sure to start at the y-intercept, not at the origin.

E X A M P L E

Graphing a line using y-intercept and slope

(0, 4)

Graph the line y

y = –3x + 4

– 3

Solution

The slope is

3, and the y-intercept is (0, 4). Be-

– 3

– 2

– 1

cause

, we use a rise of

3 and a run of 1.

– 1

To locate a second point on the line, start at (0, 4)

– 2

and go down three units and to the right one unit.

Draw a line through the two points. See Fig. 4.24.

F I G U R E 4 . 2 4

Writing the Equation for a Line

In Example 1 we wrote the equation of a line by ﬁnding its slope and y-intercept

from a graph. In the next example we write the equation of a line from a description

of the line.

E X A M P L E

Writing an equation

Write the equation in slope-intercept form for the line through (0, 4) that is perpen-

dicular to the line 2x

Solution

First ﬁnd the slope of 2x

The slope of this line is

The slope of the line that we are interested in is the opposite of the reciprocal of

So the line has slope

2 and y-intercept (0, 4). Its equation is y

c a l c u l a t o r c l o s e - u p

If you use the same minimum and maxi-

Any viewing window proportional to this

calculators have a square feature that

mum window values for x and y, then the

one will also produce approximately the

automatically makes the unit length the

length of one unit on the x-axis is larger

same unit length on each axis. Some

same on both axes.

than on the y-axis because the screen is

longer in the x-direction. In this case, per-

pendicular lines will not look perpendicu-

lar. The viewing window chosen here for

–15

the lines in Example 6 makes them look

perpendicular.

–10

Equations Of Lines In Slope-Intercept And Standard Form Worksheet Page 4

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