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Elementary Algebra

Found in: Page 540

Book edition 2nd

Author(s) Lynn Marecek, MaryAnne Anthony-Smith

Pages 1240 pages

ISBN 9780998625713

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Short Answer

Find an Equation of a Line Perpendicular to a Given Line $4 x - 3 y = 5$ contain the point is $(- 3, 2)$

The equation of the perpendicular line is $y = - \frac{3}{4} x - \frac{1}{4}$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information

The given equation is $4 x - 3 y = 5$

Step 2. Find the slope of the perpendicular line

First we find the slope of the line

$4 x - 3 y = 5$

$3 y = 4 x - 5$

$y = \frac{4}{3} x - \frac{5}{3}$

The above equation is in the form of $y = m x + c$

Then the slope of the line is $\frac{4}{3}$

Hence the slope of the perpendicular line is $- \frac{3}{4}$

Step 3. Find y- intercept

The line passes through the point is $(- 3, 2)$

We get,

$y = - \frac{3}{4} x + c$

$2 = - \frac{3}{4} (- 3) + c$

$c = - \frac{1}{4}$

The equation of the perpendicular line is $y = - \frac{3}{4} x - \frac{1}{4}$

Step 4. Conclusion

The equation of the perpendicular line is $y = - \frac{3}{4} x - \frac{1}{4}$ .

Most popular questions for Math Textbooks

Find the intercepts for $x - 3 y = 12$

Find the intercepts for $x - 2 y = 8$

In the following exercises, which ordered pair are solutions to the given equation :

$y = 2 x - 5$

(a) $(0, - 5)$ (b) $(2, 1)$ (c) $(\frac{1}{2}, - 4)$

In the following exercises, complete the table to find the solutions to each linear equation :

$y = 3 x - 1$

x	y	(x,y)
0
2
-1

Complete the table to find three solutions to this equation:

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