Question

which function is best represented by this graph?
y = \frac{1}{2}x + 3
y = -\frac{1}{2}x + 3
y = -2x + 6
y = 2x + 3

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, 3)$, so $b=3$.

Step2: Calculate slope

Use two points: $(0,3)$ and $(6,0)$. Slope $m=\frac{0-3}{6-0}=-\frac{1}{2}$.

Step3: Form linear equation

Substitute $m$ and $b$ into $y=mx+b$.
$y=-\frac{1}{2}x+3$

Step4: Match with options

Compare to given choices.

Answer:

$\boldsymbol{y = -\frac{1}{2}x + 3}$