Question

graph this line:
$y + 2 = \frac{1}{3}(x + 2)$
click to select points on the graph.

Explanation:

Step1: Identify point from point-slope form

The equation $y + 2 = \frac{1}{3}(x + 2)$ is in point-slope form $y - y_1 = m(x - x_1)$, so one point on the line is $(-2, -2)$.

Step2: Find a second point using slope

The slope $m = \frac{1}{3}$, meaning from $(-2, -2)$, move 3 right and 1 up:
$x = -2 + 3 = 1$, $y = -2 + 1 = -1$. So a second point is $(1, -1)$.

Step3: Verify with y-intercept (optional)

Rewrite in slope-intercept form:
$y = \frac{1}{3}x + \frac{2}{3} - 2$
$y = \frac{1}{3}x - \frac{4}{3}$
When $x=0$, $y = -\frac{4}{3} \approx -1.33$, which aligns with the line through the two points.

Answer:

Plot the points $(-2, -2)$ and $(1, -1)$, then draw a straight line passing through them. This line represents the equation $y + 2 = \frac{1}{3}(x + 2)$.