Question

graph a line that contains the point $(-2, -3)$ and has a slope of $\frac{8}{7}$.

Explanation:

Step1: Find line equation (point-slope)

Use point-slope form $y-y_1=m(x-x_1)$ where $(x_1,y_1)=(-2,-3)$, $m=\frac{8}{7}$:
$y-(-3)=\frac{8}{7}(x-(-2))$
Simplify: $y+3=\frac{8}{7}(x+2)$

Step2: Convert to slope-intercept form

Expand and isolate $y$:
$y=\frac{8}{7}x + \frac{16}{7} - 3$
$y=\frac{8}{7}x + \frac{16}{7} - \frac{21}{7}$
$y=\frac{8}{7}x - \frac{5}{7}$

Step3: Identify second point

From $(-2,-3)$, use slope $\frac{8}{7}$: move 7 right, 8 up:
$x=-2+7=5$, $y=-3+8=5$ → point $(5,5)$

Step4: Plot and connect points

Plot $(-2,-3)$ and $(5,5)$, draw a straight line through them.

Answer:

The line with equation $y=\frac{8}{7}x - \frac{5}{7}$, passing through $(-2,-3)$ and $(5,5)$, graphed as a straight line through these two points.