Question

which function is best represented by this graph?
y = 1x + 4
y = 4x + 2
y = 2x
y = \frac{1}{4}x + 2

Explanation:

Step1: Identify y-intercept

The graph crosses the y-axis at $(0, 2)$, so $b=2$. Eliminate options without $b=2$: $y=1x+4$ and $y=2x$ are ruled out.

Step2: Calculate slope

Pick two points on the line, e.g., $(0,2)$ and $(4,3)$. Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$.
$m=\frac{3-2}{4-0}=\frac{1}{4}$

Step3: Match to function

The slope-intercept form is $y=mx+b$. Substitute $m=\frac{1}{4}$ and $b=2$: $y=\frac{1}{4}x+2$.

Answer:

$\boldsymbol{y = \frac{1}{4}x + 2}$