Question

find the lines slope and a point on the line.
$y + 4 = -\frac{2}{3}(x - 4)$
slope:
point on the line:

Explanation:

Step1: Recall point-slope form

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

Step2: Identify the slope

Compare $y+4 = -\frac{2}{3}(x-4)$ to $y - y_1 = m(x - x_1)$. Here, $m = -\frac{2}{3}$.

Step3: Identify the point

Rewrite $y+4$ as $y - (-4)$. So $x_1=4$, $y_1=-4$, giving the point $(4, -4)$.

Answer:

slope: $-\frac{2}{3}$
point on the line: $(4, -4)$