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Found in: Page 540

Elementary Algebra

Book edition 2nd
Author(s) Lynn Marecek, MaryAnne Anthony-Smith
Pages 1240 pages
ISBN 9780998625713

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

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

See the step by step solution

Step 1. Given information

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

Step 2. Find the slope of the perpendicular  line

First we find the slope of the line

$4x-3y=5$

$3y=4x-5$

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

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

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 $\left(-3,2\right)$

We get,

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

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

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

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 $y=-\frac{3}{4}x-\frac{1}{4}$.