Question

choose all that correctly graphs the function.
a
$f(x) = \frac{1}{5}x - 2$
b
$f(x) = \frac{2}{3}x + 3$

Explanation:

Step1: Analyze Function A

The function is $f(x)=\frac{1}{5}x - 2$. This is a linear function in the form $y=mx+b$, where $m$ (slope) is $\frac{1}{5}$ and $b$ (y-intercept) is $-2$.

• Y-intercept: The line should cross the y-axis at $(0, -2)$, which matches graph A.
• Slope: A slope of $\frac{1}{5}$ means for every 5 units right, the line rises 1 unit. The line in graph A shows this shallow positive slope, so it is correct.

Step2: Analyze Function B

The function is $f(x)=\frac{2}{3}x + 3$. Here, $m=\frac{2}{3}$ and $b=3$.

• Y-intercept: The line should cross the y-axis at $(0, 3)$, which matches graph B.
• Slope: A slope of $\frac{2}{3}$ means for every 3 units right, the line rises 2 units. The line in graph B shows this moderate positive slope, so it is correct.

Answer:

A. Graph matching $f(x)=\frac{1}{5}x - 2$, B. Graph matching $f(x)=\frac{2}{3}x + 3$