Question

graph $y = \frac{4}{5}x - 7$.

Explanation:

Step1: Identify slope-intercept form

The equation $y = \frac{4}{5}x - 7$ uses the slope-intercept form $y=mx+b$, where $m=\frac{4}{5}$ (slope) and $b=-7$ (y-intercept).

Step2: Plot the y-intercept

The y-intercept is the point where $x=0$, so substitute $x=0$:
$y = \frac{4}{5}(0) - 7 = -7$
This gives the point $(0, -7)$.

Step3: Use slope to find a second point

The slope $\frac{4}{5}$ means $\frac{\text{rise}}{\text{run}} = \frac{4}{5}$. From $(0, -7)$, move 5 units right (run) and 4 units up (rise):
New $x = 0 + 5 = 5$, New $y = -7 + 4 = -3$
This gives the point $(5, -3)$.

Step4: Draw the line

Connect the points $(0, -7)$ and $(5, -3)$, then extend the line in both directions across the grid.

Answer:

The line passes through points $(0, -7)$ and $(5, -3)$, and extends infinitely in both directions on the coordinate plane.