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

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

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

Answer

Answer:

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

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0,1)$, so $b=1$.

Step2: Calculate slope $m$

Use points $(-4,3)$ and $(4,-1)$: $m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-3}{4-(-4)}=\frac{-4}{8}=-\frac{1}{2}$

Step3: Write linear function

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