Question

write the equation of the line described below in point - slope form.
find the equation of the line that is parallel to the line $y = - 4x - 5$ and passes through the point $(5, - 9)$. write the equation in point - slope form.

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. For $y = -4x -5$, the slope $m = -4$.

Step2: Apply point-slope formula

Point-slope form is $y - y_1 = m(x - x_1)$. Substitute $m=-4$, $x_1=5$, $y_1=-9$.
<Expression>
$y - (-9) = -4(x - 5)$
</Expression>

Step3: Simplify the left side

Simplify the double negative term.
<Expression>
$y + 9 = -4(x - 5)$
</Expression>

Answer:

$y + 9 = -4(x - 5)$