Question

which graph correctly shows the graph of the following line? $y = \frac{1}{2}x + 4$ (and an image of a coordinate grid with a line graph)

Explanation:

Step1: Identify y-intercept

The equation is in slope-intercept form $y=mx+b$, where $b=4$. So the line crosses the y-axis at $(0, 4)$.

Step2: Identify slope

The slope $m=\frac{1}{2}$, meaning for every 2-unit increase in $x$, $y$ increases by 1. From $(0,4)$, moving right 2, up 1 gives $(2, 5)$.

Step3: Compare to given graph

The provided graph has a y-intercept at $(4,0)$ (swapped axes) and slope $\frac{2}{1}$, which does not match $y=\frac{1}{2}x+4$. This graph is incorrect.

Answer:

The provided graph does NOT correctly show $y=\frac{1}{2}x+4$. A correct graph would cross the y-axis at $(0,4)$ and pass through points like $(2,5)$, $(4,6)$, $(-2,3)$.