Question

graph this line:
$y + 3 = -\frac{6}{5}(x + 3)$
click to select points on the graph.

Explanation:

Step1: Identify point from point-slope form

The equation $y + 3 = -\frac{6}{5}(x + 3)$ is in point-slope form $y - y_1 = m(x - x_1)$, so the point $(x_1, y_1)$ is $(-3, -3)$.

Step2: Use slope to find second point

The slope $m = -\frac{6}{5}$, meaning $\frac{\text{change in } y}{\text{change in } x} = \frac{-6}{5}$. Starting from $(-3, -3)$, add 5 to $x$ and subtract 6 from $y$:
$x = -3 + 5 = 2$, $y = -3 - 6 = -9$. So the second point is $(2, -9)$.

Step3: Verify with y-intercept (optional)

Rewrite equation to slope-intercept form:
$y = -\frac{6}{5}x - \frac{18}{5} - 3$
$y = -\frac{6}{5}x - \frac{18}{5} - \frac{15}{5}$
$y = -\frac{6}{5}x - \frac{33}{5}$
When $x=0$, $y = -\frac{33}{5} = -6.6$, so the y-intercept is $(0, -6.6)$.

Answer:

Plot the points $(-3, -3)$, $(2, -9)$, and $(0, -6.6)$, then draw a straight line through them to graph the line.