what is the equation of the line that passes through the point $(-3,-8)$ and has a slope of 4?

Explanation:

Step1: Use point-slope form

The point-slope formula is $y - y_1 = m(x - x_1)$, where $m=4$, $x_1=-3$, $y_1=-8$. Substitute values: $y - (-8) = 4(x - (-3))$

Step2: Simplify the equation

Simplify signs: $y + 8 = 4(x + 3)$ Expand right side: $y + 8 = 4x + 12$

Step3: Isolate y to get slope-intercept form

Subtract 8 from both sides: $y = 4x + 12 - 8$ Simplify constants: $y = 4x + 4$

Answer:

$y = 4x + 4$