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

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear function is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The y - intercept is the value of $y$ when $x = 0$. From the graph, when $x = 0$, $y=1$, so $b = 1$.

Step2: Calculate the slope

The slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points from the graph, say $(0,1)$ and $(4, - 1)$. Then $m=\frac{-1 - 1}{4-0}=\frac{-2}{4}=-\frac{1}{2}$.

Step3: Write the linear function

Substitute $m =-\frac{1}{2}$ and $b = 1$ into $y=mx + b$. We get $y=-\frac{1}{2}x + 1$, or $f(x)=-\frac{1}{2}x + 1$.

Answer:

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