Question

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

$\circ \\ \frac{2}{9}$

$\circ \\ \frac{1}{3}$ (negative?)

$\circ \\ \frac{1}{3}$

$\circ \\ \frac{2}{9}$

Explanation:

Step1: Recall the 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 form $y = mx + b$.

Step2: Identify the y - intercept

In the equation $f(x)=-\frac{2}{9}x+\frac{1}{3}$, when we compare it to $y=mx + b$, the value of $b$ (the $y$-intercept) is $\frac{1}{3}$. We can also find the $y$-intercept by setting $x = 0$ in the function. If $x = 0$, then $f(0)=-\frac{2}{9}(0)+\frac{1}{3}=\frac{1}{3}$.

Answer:

C. $\frac{1}{3}$ (assuming the third option is labeled as C, if the options are labeled as A: $\frac{2}{9}$, B: $-\frac{1}{3}$, C: $\frac{1}{3}$, D: $\frac{2}{9}$)