Question

a line passes through the point $(-4, 4)$ and has a slope of $-\frac{3}{2}$. write an equation in point - slope form for this line.

Explanation:

Step1: Recall point-slope formula

The point-slope form of a line is $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope.

Step2: Substitute given values

Substitute $x_1 = -4$, $y_1 = 4$, and $m = -\frac{3}{2}$ into the formula:
$y - 4 = -\frac{3}{2}(x - (-4))$

Step3: Simplify the x-term

Simplify $x - (-4)$ to $x + 4$:
$y - 4 = -\frac{3}{2}(x + 4)$

Answer:

$y - 4 = -\frac{3}{2}(x + 4)$