Question

write the equation of the line described below in point - slope form.
find the equation of the line that is perpendicular to the line ( y = 5x - 4 ) and passes through the point ( (-4, -10) ). write the equation in point - slope form.

Explanation:

Step1: Find perpendicular slope

The slope of $y=5x-4$ is $5$. The slope of a perpendicular line is the negative reciprocal: $m = -\frac{1}{5}$

Step2: Apply point-slope formula

Point-slope form is $y - y_1 = m(x - x_1)$, use $(x_1,y_1)=(-4,-10)$ and $m=-\frac{1}{5}$.
$y - (-10) = -\frac{1}{5}(x - (-4))$

Step3: Simplify signs

$y + 10 = -\frac{1}{5}(x + 4)$

Answer:

$y + 10 = -\frac{1}{5}(x + 4)$