Question

graph this line:
$y - 6 = -\frac{7}{4}(x + 6)$
click to select points on the graph.

Explanation:

Step1: Identify point from point-slope form

The equation $y - 6 = -\frac{7}{4}(x + 6)$ is in point-slope form $y-y_1=m(x-x_1)$, where $(x_1,y_1)=(-6,6)$.

Step2: Find a second point using slope

Slope $m=-\frac{7}{4}$ means $\frac{\Delta y}{\Delta x}=-\frac{7}{4}$. Starting from $(-6,6)$, add 4 to $x$ and subtract 7 from $y$:
$x=-6+4=-2$, $y=6-7=-1$. So the second point is $(-2,-1)$.

Step3: Verify with y-intercept (optional)

Rewrite equation to slope-intercept form:
$y = -\frac{7}{4}x - \frac{42}{4} + 6 = -\frac{7}{4}x - \frac{42}{4} + \frac{24}{4} = -\frac{7}{4}x - \frac{18}{4} = -\frac{7}{4}x - \frac{9}{2}$
When $x=0$, $y=-\frac{9}{2}=-4.5$, giving the point $(0,-4.5)$.

Answer:

Plot the points $(-6, 6)$, $(-2, -1)$, and $(0, -4.5)$, then draw a straight line through them.