Question

graph the line with the equation $y = -\frac{1}{5}x - 3$.

Explanation:

Step1: Identify y-intercept

The equation $y = -\frac{1}{5}x - 3$ is in slope-intercept form $y=mx+b$, where $b$ is the y-intercept. Here, $b=-3$, so the line crosses the y-axis at $(0, -3)$.

Step2: Find second point using slope

The slope $m = -\frac{1}{5}$, meaning $\frac{\text{rise}}{\text{run}} = \frac{-1}{5}$. Starting from $(0, -3)$, move 5 units right (run = 5) and 1 unit down (rise = -1) to get the point $(0+5, -3-1) = (5, -4)$.

Step3: Plot and connect points

Plot the points $(0, -3)$ and $(5, -4)$, then draw a straight line through them (extending it across the grid).

Answer:

The line passes through points $(0, -3)$ and $(5, -4)$, and extends infinitely in both directions across the coordinate grid.