Question

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

Explanation:

Step1: Identify slope and y - intercept

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

Step2: Plot the y - intercept

The y - intercept is the point where the line crosses the y - axis. Plot the point $(0, - 2)$.

Step3: Use the slope to find another point

The slope $m =-\frac{1}{3}=\frac{\text{rise}}{\text{run}}$. From the point $(0,-2)$, move 1 unit down (rise = - 1) and 3 units to the right (run = 3) to get the point $(3,-3)$.

Step4: Draw the line

Connect the two points $(0, - 2)$ and $(3,-3)$ with a straight line.

Answer:

Graph a line passing through the points $(0,-2)$ and $(3,-3)$ on the given coordinate axes.