   Chapter 10.5, Problem 22E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 9 to 24, find an equation of the line described. Leave the solution in the form Ax+By = C .The line contains (2,-3) and is perpendicular to the line 2 x - 3 y = 6 .

To determine

Find the equation of the line contains (2,-3) and is perpendicular to the line 2x-3y=6.

Explanation

The general equation of a line is y=mx+b

Let m1 be the slope of the given parallel line

Let m2 be the slope of the line for which the equation to be found.

The given line equation 2x-3y=6 can be modified to find its slope.

2x-3y=6 can be rewritten as,

-3y=-2x+6

Then,

y=-2x+6-3

y=-2x-3+6-3

y=2x3-2

y=23x-2

Compare y=23x-2 with the general equation. Then,

m1=23

Since the lines are perpendicular,

m2=-1m1

Hence,

m2=-32

From the given coordinates,

x1=2

y1=-3

Substitute x1, y1, and m2 in the general equation to find the equation of the unknown line

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