Question

graph the line with the equation $y = \frac{1}{4}x + 7$.

Explanation:

Step1: Identify y-intercept

The equation is in slope-intercept form $y=mx+b$, where $b=7$. So the y-intercept is the point $(0, 7)$.

Step2: Use slope to find second point

Slope $m=\frac{1}{4}$, meaning $\frac{\text{rise}}{\text{run}}=\frac{1}{4}$. From $(0,7)$, move 4 units right and 1 unit up to get the point $(4, 8)$.

Step3: Plot and connect points

Plot $(0,7)$ and $(4,8)$, then draw a straight line through them. Extend the line across the grid.

Answer:

The line passes through points $(0, 7)$ and $(4, 8)$, extending infinitely in both directions across the coordinate grid.