Question

which function is graphed here? graph of a line \\(\circ f(x) = -\frac{1}{2}x + 2\\) \\(\circ f(x) = -\frac{1}{3}x + 2\\) \\(\circ f(x) = -\frac{1}{2}x + 5\\) \\(\circ f(x) = \frac{1}{3}x + 2\\)

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, 2)$, so $b=2$.

Step2: Calculate slope

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

Step3: Form linear equation

Use $y=mx+b$: $f(x)=-\frac{1}{3}x+2$.

Step4: Match with options

Compare to given choices.

Answer:

$f(x)=-\frac{1}{3}x+2$ (the second option)