Question

graph this line:
$y - 2 = -\frac{5}{4}(x + 4)$
click to select points on the graph.

Explanation:

Step1: Identify point from point-slope form

The equation $y - 2 = -\frac{5}{4}(x + 4)$ is in point-slope form $y-y_1=m(x-x_1)$, where $(x_1,y_1)=(-4,2)$.

Step2: Find a second point using slope

Slope $m=-\frac{5}{4}$, meaning $\frac{\Delta y}{\Delta x}=-\frac{5}{4}$. Starting at $(-4,2)$, add 4 to $x$ and subtract 5 from $y$:
$x=-4+4=0$, $y=2-5=-3$. So the second point is $(0,-3)$.

Step3: Verify with a third point (optional)

From $(0,-3)$, add 4 to $x$ and subtract 5 from $y$:
$x=0+4=4$, $y=-3-5=-8$. Third point: $(4,-8)$.

Answer:

Plot the points $(-4, 2)$, $(0, -3)$, and $(4, -8)$, then draw a straight line through them to graph the line.