Question

which is the graph of $y - 3 = -\frac{2}{3}(x + 6)$?

Explanation:

Step1: Convert to slope-intercept form

Start with the given equation:
$$y - 3 = -\frac{2}{3}(x + 6)$$
Distribute $-\frac{2}{3}$:
$$y - 3 = -\frac{2}{3}x - 4$$
Add 3 to both sides:
$$y = -\frac{2}{3}x - 1$$

Step2: Identify key points

1. y-intercept: When $x=0$, $y = -\frac{2}{3}(0) - 1 = -1$. So the line passes through $(0, -1)$.
2. Check another point: When $x=3$, $y = -\frac{2}{3}(3) - 1 = -2 - 1 = -3$. So the line passes through $(3, -3)$.

Step3: Match points to graphs

Compare the points $(0, -1)$ and $(3, -3)$ to the provided graphs. The first graph contains both of these points.

Answer:

The first graph (with points $(-3,1)$, $(0,-1)$, $(3,-3)$)