Question

which graph represents the linear equation $y=\frac{1}{2}x-2$ on the coordinate plane?

Explanation:

Step1: Identify slope and y-intercept

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

Step2: Locate y-intercept on graph

The y-intercept $b=-2$ means the line crosses the y-axis at the point $(0, -2)$.

Step3: Use slope to find next point

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

Step4: Verify line characteristics

The positive slope $\frac{1}{2}$ means the line rises from left to right.

Answer:

The graph is a straight line that crosses the y-axis at $(0, -2)$, rises from left to right, and passes through the point $(2, -1)$.