Question

which equation gives the line shown on the graph?
options:
y = 2x + 4
y = -\frac{1}{2}x - 4
y = 2x - 4
y = \frac{1}{2}x + 4

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, 4)$, so $b=4$.

Step2: Calculate slope

Use two points $(0,4)$ and $(2,5)$. Slope $m=\frac{5-4}{2-0}=\frac{1}{2}$.

Step3: Write line equation

Substitute $m=\frac{1}{2}$ and $b=4$ into $y=mx+b$.
$y=\frac{1}{2}x+4$

Step4: Match with options

The derived equation matches the last option.

Answer:

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