   Chapter 10.4, Problem 24E 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

Use the result in Exercise 21 to find the equation of the line that contains ( 5 , - 1 ) and is perpendicular to the graph of 3 x - 4 y = 12 .

To determine

To find:

The equation of the line that contains (5,-1) and is perpendicular to the graph of 3x-4y=12.

Explanation

Given equation is,

3x-4y=12

Given point is, (5,-1)

To find the equation of the point (5,-1) perpendicular to the equation 3x-4y=12, follow as below,

First needed to find the slope of the given equation,

3x-4y=12

Formula for finding the slope:

y=mx+c

Here, m is the slope.

-4y=12-3x

Divided by 4 on both sides of the above equation,

y=-12-3x4

y=-124+3x4

y=-3+3x4

Where, m1=34

Since the lines are perpendicular, slope m2 of the line crossing through the point (4, 5) is,

Condition for the equations to be perpendicular is,

m1·m2=-1

34·m2

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