Question

which point - slope equation represents a line that passes through (3, -2) with a slope of $-\frac{4}{5}$?
$y - 3 = -\frac{4}{5}(x + 2)$
$y - 2 = \frac{4}{5}(x - 3)$
$y + 2 = -\frac{4}{5}(x - 3)$
$y + 3 = \frac{4}{5}(x + 2)$

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

We have $(x_1, y_1)=(3, -2)$ and $m=-\frac{4}{5}$. Substitute into the formula:
$y - (-2) = -\frac{4}{5}(x - 3)$

Step3: Simplify the equation

Simplify the left-hand side:
$y + 2 = -\frac{4}{5}(x - 3)$

Answer:

$y + 2 = -\frac{4}{5}(x - 3)$