Question

What is the slope of any line perpendicular to the line $-5x+3y=9$?

• A. $-\frac{3}{5}$
• B. $\frac{5}{3}$
• C. $\frac{3}{5}$
• D. $-\frac{5}{3}$
• E. $-\frac{1}{3}$

Answer 1

The correct option is A $-\frac{3}{5}$

Write the equation of the given line and find the slope as follows:

$-5x+3y=9$

$\Rightarrow 3y=5x+9$

$\Rightarrow y=\frac{5}{3}x+3$

Therefore, the slope is $\frac{5}{3}$.

Slope $m$ of the perpendicular is such that $\frac{5}{3}m=-1$

$\Rightarrow m=-\frac{3}{5}$

Hence, option A is correct.