Question

graph the line with the equation $y = -\frac{1}{3}x - 2$.

Explanation:

Step1: Identify slope and y-intercept

The equation $y = -\frac{1}{3}x - 2$ is in slope-intercept form $y=mx+b$, where $m=-\frac{1}{3}$ (slope) and $b=-2$ (y-intercept).

Step2: Plot the y-intercept

The y-intercept is the point where $x=0$, so the point is $(0, -2)$. Mark this on the graph.

Step3: Use slope to find a second point

Slope $m=\frac{\text{rise}}{\text{run}}=-\frac{1}{3}$. From $(0, -2)$, move down 1 unit and right 3 units, or up 1 unit and left 3 units. This gives the point $(3, -3)$ (or $(-3, -1)$). Mark this second point.

Step4: Draw the line

Connect the two plotted points with a straight line, extending it across the entire grid.

Answer:

The line passes through points $(0, -2)$ and $(3, -3)$ (or equivalent points) and extends infinitely in both directions on the coordinate plane.