Question

y + 5 = \frac{1}{3}(x + 8) click to select points on the graph.

Explanation:

Step1: Identify point from equation

The given equation is in point-slope form $y - y_1 = m(x - x_1)$, so one point is $(-8, -5)$.

Step2: Find second point using slope

Slope $m=\frac{1}{3}$. From $(-8, -5)$, add 3 to $x$ and 1 to $y$:
$x=-8+3=-5$, $y=-5+1=-4$. So second point is $(-5, -4)$.

Step3: Verify with y-intercept

Rewrite equation to slope-intercept form:
$y + 5 = \frac{1}{3}(x + 8)$
$y = \frac{1}{3}x + \frac{8}{3} - 5$
$y = \frac{1}{3}x + \frac{8}{3} - \frac{15}{3}$
$y = \frac{1}{3}x - \frac{7}{3}$
When $x=0$, $y=-\frac{7}{3}\approx-2.33$, which is a third point on the line.

Answer:

The line passes through the points $(-8, -5)$, $(-5, -4)$, and $(0, -\frac{7}{3})$ (or approximately $(0, -2.33)$). Plot these points and draw a straight line through them to graph the equation.