Question

1. write an equation of the line that passes through the point (-4, -13) and is parallel to the line y = -3x + 5.

Explanation:

Step1: Identify parallel slope

Parallel lines have equal slopes. The given line $y=-3x+5$ has slope $m=-3$, so the new line also has $m=-3$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m=-3$, $x_1=-4$, $y_1=-13$:
$y - (-13) = -3(x - (-4))$

Step3: Simplify to slope-intercept form

Simplify the equation:
$y + 13 = -3(x + 4)$
$y + 13 = -3x -12$
$y = -3x -12 -13$
$y = -3x -25$

Answer:

$y = -3x -25$