Question

give the slope and y - intercept of the line whose equation is given. then graph the linear function.
$f(x)=\frac{2}{3}x - 3$
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the slope is \square.
(simplify your answer. type an integer or a fraction.)
b. the slope is undefined.
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the y - intercept is \square.
(simplify your answer. type an integer or a fraction.)
b. there is no y - intercept.
use the graphing tool to graph the equation.
click to enlarge graph

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The given function is $f(x)=\frac{2}{3}x - 3$. We can rewrite $y=f(x)$, so the equation is in the form $y=\frac{2}{3}x-3$.

Step2: Determine the slope

Comparing $y=\frac{2}{3}x - 3$ with $y = mx + b$, we see that $m=\frac{2}{3}$. So the slope is $\frac{2}{3}$, which means option A is correct for the slope part.

Step3: Determine the y - intercept

Again, comparing $y=\frac{2}{3}x - 3$ with $y=mx + b$, we see that $b=- 3$. So the y - intercept is $-3$, which means option A is correct for the y - intercept part.

Answer:

(for slope):
A. The slope is $\frac{2}{3}$.