Question

the equation of line lm is $5x - y = -4$. what is the equation of a line perpendicular to line lm in slope - intercept form that contains point $(-3, 2)$?
$\bigcirc$ $y = 5x + 13$
$\bigcirc$ $y = -\frac{1}{5}x + \frac{7}{5}$
$\bigcirc$ $y = -\frac{1}{5}x - \frac{7}{5}$
$\bigcirc$ $y = 5x - 17$

Explanation:

Step1: Rewrite LM to slope-intercept form

Rearrange $5x - y = -4$ to $y = 5x + 4$.

Step2: Find perpendicular slope

Perpendicular slope is negative reciprocal: $m = -\frac{1}{5}$.

Step3: Solve for y-intercept b

Substitute $x=-3, y=2, m=-\frac{1}{5}$ into $y=mx+b$:
$2 = -\frac{1}{5}(-3) + b$
$2 = \frac{3}{5} + b$
$b = 2 - \frac{3}{5} = \frac{10}{5} - \frac{3}{5} = \frac{7}{5}$

Step4: Write final equation

Combine slope and intercept: $y = -\frac{1}{5}x + \frac{7}{5}$

Answer:

B. $y = -\frac{1}{5}x + \frac{7}{5}$