Question

1. $y = \frac{1}{3}x - 2$

Explanation:

Step1: Identify y-intercept

The equation $y=\frac{1}{3}x-2$ is in slope-intercept form $y=mx+b$, where $b=-2$. So the y-intercept is the point $(0, -2)$.

Step2: Find a second point

Use the slope $m=\frac{1}{3}$ (rise 1, run 3). Starting from $(0, -2)$, add 3 to $x$ and 1 to $y$:
$x=0+3=3$, $y=-2+1=-1$.
This gives the point $(3, -1)$.

Step3: Plot and connect points

Mark $(0, -2)$ and $(3, -1)$ on the grid, then draw a straight line through them, extending it across the coordinate plane.

Answer:

The line $y=\frac{1}{3}x-2$ is graphed by plotting the y-intercept $(0, -2)$ and the point $(3, -1)$, then drawing a straight line through these points (extending in both directions).