Question

graph this line:
$y - 3 = 3(x + 1)$
click to select points on the graph.

Explanation:

Step1: Rewrite to slope-intercept form

First, expand and isolate $y$:

$$\begin{align*} y - 3 &= 3(x + 1)\\ y - 3 &= 3x + 3\\ y &= 3x + 6 \end{align*}$$

Step2: Identify y-intercept

The y-intercept is when $x=0$:
$$y = 3(0) + 6 = 6$$
So the point is $(0, 6)$.

Step3: Find a second point

Use slope $m=3$ (rise 3, run 1). From $(0,6)$, add 1 to $x$ and 3 to $y$:
$$(0+1, 6+3) = (1, 9)$$
Or use $x=-2$ to find another point:
$$y = 3(-2) + 6 = 0$$
So the point is $(-2, 0)$.

Answer:

Plot the points $(0, 6)$ and $(-2, 0)$ (or $(1, 9)$), then draw a straight line through them. The line represents $y = 3x + 6$.