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 $m$ (slope) $=\frac{4}{5}$ and $b$ (y-intercept) $=-7$.

Step2: Plot the y-intercept

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

Step3: Use slope to find a second point

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 $(5, -3)$ with a straight line, extending it in both directions.

Answer:

The graph is a straight line passing through the points $(0, -7)$ and $(5, -3)$, following the equation $y=\frac{4}{5}x-7$.