Question

graph this line:
$y + 6 = \frac{2}{3}(x + 5)$
click to select points on the graph.

Explanation:

Step1: Identify point from point-slope form

The equation $y + 6 = \frac{2}{3}(x + 5)$ is in point-slope form $y - y_1 = m(x - x_1)$, so one point is $(x_1, y_1) = (-5, -6)$.

Step2: Find a second point using slope

Slope $m = \frac{2}{3}$, meaning from $(-5, -6)$, move 3 right and 2 up:
$x = -5 + 3 = -2$, $y = -6 + 2 = -4$.
Second point: $(-2, -4)$.

Step3: Verify with y-intercept (optional)

Rewrite to slope-intercept form:
$y = \frac{2}{3}x + \frac{10}{3} - 6$
$y = \frac{2}{3}x + \frac{10}{3} - \frac{18}{3}$
$y = \frac{2}{3}x - \frac{8}{3}$
Y-intercept: $(0, -\frac{8}{3}) \approx (0, -2.67)$

Answer:

Plot the points $(-5, -6)$, $(-2, -4)$, and $(0, -\frac{8}{3})$, then draw a straight line through them to graph the line.