ANSWER:
Y intercept: (0, 2)
X intercept: (-8, 0)
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]y=\frac{1}{4}x+2[/tex]We have that x-intercept is the point when y is equal to 0 and y-intercept is point when x is equal to 0, therefore:
[tex]\begin{gathered} \text{ x-intercept} \\ 0=\frac{1}{4}x+2 \\ \frac{1}{4}x=-2 \\ x=4\cdot-2=-8\rightarrow(-8,0) \\ \text{y-intercept} \\ y=\frac{1}{4}\cdot0+2 \\ y=2\rightarrow(0,2) \end{gathered}[/tex]