Question

graph this line:
$y - 7 = -\frac{2}{3}(x + 7)$
click to select points on the graph.

Explanation:

Step1: Identify point from point-slope form

The equation $y - 7 = -\frac{2}{3}(x + 7)$ is in point-slope form $y-y_1=m(x-x_1)$, so one point is $(-7, 7)$.

Step2: Find a second point using slope

Slope $m=-\frac{2}{3}$ means $\frac{\Delta y}{\Delta x}=-\frac{2}{3}$. From $(-7,7)$, add 3 to $x$ and subtract 2 from $y$:
$x=-7+3=-4$, $y=7-2=5$. So a second point is $(-4, 5)$.

Step3: Verify with y-intercept (optional)

Rewrite equation to slope-intercept form:
$y = -\frac{2}{3}x - \frac{14}{3} + 7$
$y = -\frac{2}{3}x + \frac{7}{3}$
The y-intercept is $(0, \frac{7}{3}) \approx (0, 2.33)$, which lies on the line through the two points.

Answer:

Plot the points $(-7, 7)$ and $(-4, 5)$ (or $(0, \frac{7}{3})$), then draw a straight line through them to graph the equation.