Question

graph the line with the equation $y = \frac{1}{2}x + 5$.

Explanation:

Step1: Identify y-intercept

The equation is in slope-intercept form $y=mx+b$, where $b=5$. So the line crosses the y-axis at $(0, 5)$.

Step2: Use slope to find 2nd point

Slope $m=\frac{1}{2}$, meaning $\frac{\text{rise}}{\text{run}}=\frac{1}{2}$. From $(0,5)$, move up 1, right 2 to get $(2, 6)$.

Step3: Plot and connect points

Mark $(0,5)$ and $(2,6)$ on the grid, then draw a straight line through them (extending in both directions).

Answer:

The line passes through the y-intercept $(0, 5)$ and has a slope of $\frac{1}{2}$, so it can be graphed by plotting $(0,5)$ and a second point (e.g., $(2,6)$) then drawing a straight line through these points.