Question

which linear function is represented by the graph?
○ $f(x) = -2x + 1$
○ $f(x) = -\frac{1}{2}x + 1$
○ $f(x) = \frac{1}{2}x + 1$
○ $f(x) = 2x + 1$

Explanation:

Step1: Identify slope formula

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$
Pick points $(0,1)$ and $(4,-1)$: $m=\frac{-1-1}{4-0}=\frac{-2}{4}=-\frac{1}{2}$

Step2: Find y-intercept

From graph, $b=1$ (when $x=0$, $y=1$)

Step3: Write linear function

Substitute $m$ and $b$ into $f(x)=mx+b$: $f(x)=-\frac{1}{2}x+1$

Answer:

$\boldsymbol{f(x)=-\frac{1}{2}x + 1}$ (Option B)