   Chapter 10.4, Problem 25E 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 20 to find the equation of the line that contains ( 4, 5 ) and is perpendicular to the graph of 2 x + 3 y = 6 .

To determine

To find:

The equation of the line that contains (4, 5) and is perpendicular to the graph of 2x+3y=6.

Explanation

Given equation is, 2x+3y=6

Given point is, (4, 5)

To find the equation of the point (4, 5) perpendicular to the equation 2x+3y=6 follow as below,

First needed to find the slope of the given equation,

2x+3y=6

Formula for finding the slope:

y=mx+c

Here, m is the slope.

3y=6-2x

Divided by 3 on both sides of the above equation,

y=6-2x3

y=63-2x3

y=2-2x3

Where, m1=-23

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

-23·m2=-1

m

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