Question

which of the following is the graph of this function rule? y = \frac{x}{4} + 3

Explanation:

Step1: Identify y-intercept

The function is in slope-intercept form $y=mx+b$, where $b=3$. So the line crosses the y-axis at $(0, 3)$.

Step2: Find a second point

Substitute $x=4$ into the function:
$y = \frac{4}{4} + 3 = 1 + 3 = 4$
This gives the point $(4, 4)$.

Step3: Match points to graphs

Check which graph has points $(0, 3)$ and $(4, 4)$. The first graph contains these points, with a positive, shallow slope matching $m=\frac{1}{4}$.

Answer:

The first graph (leftmost graph with points at (0, 3) and (4, 4), showing a shallow upward-sloping line)