Question

what is the y-intercept of the function $f(x) = -\frac{2}{9}x + \frac{1}{3}$?
$-\frac{2}{9}$
$-\frac{1}{3}$
$\frac{1}{3}$
$\frac{2}{9}$

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. In the function $f(x)=-\frac{2}{9}x+\frac{1}{3}$, we can compare it with the general form $y = mx + b$.

Step2: Identify the y - intercept

By comparing $f(x)=-\frac{2}{9}x+\frac{1}{3}$ with $y = mx + b$, we see that $m = -\frac{2}{9}$ (the slope) and $b=\frac{1}{3}$. The value of $b$ in the slope - intercept form is the $y$-intercept.

Answer:

$\frac{1}{3}$ (corresponding to the option " $\boldsymbol{\frac{1}{3}}$")