Question

which graph matches the equation $y+3=2(x+3)$?

Explanation:

Step1: Rewrite to slope-intercept form

First, expand and isolate $y$:

$$\begin{align*} y+3&=2(x+3)\\ y+3&=2x+6\\ y&=2x+6-3\\ y&=2x+3 \end{align*}$$

Step2: Identify key features

The line has a slope of $2$ and a y-intercept at $(0, 3)$. We can also verify the point from the point-slope form: when $x=-3$, $y=-3$, so $(-3, -3)$ lies on the line.

Step3: Match to the graph

The top graph includes the points $(0, 3)$ and $(-3, -3)$, and has a positive slope of $2$, which matches the equation.

Answer:

The top graph (the one passing through points $(0, 3)$ and $(-3, -3)$) matches the equation $y+3=2(x+3)$.