# Chapter 4 - Section 4.1 - Properties of Linear Functions and Linear Models - 4.1 Assess Your Understanding: 17

a) Slope $=\frac{1}{4}$ and y-intercept $=−3$ (b) See the image. (c) Average rate of change $=\frac{1}{4}=0.25$ (d) The linear function $f(x)=\frac{1}{4}x−3$ is increasing.

#### Work Step by Step

Step-1: Compare the given equation with the slope-intercept form of the linear equation, that is, $f(x)=mx+b$, where $m$ is the slope of the linear function and $b$ is its y-intercept. By comparing $$f(x)=\frac{1}{4}x−3$$ to $$f(x)=mx+b$$ we understand that the slope of the given function is −3. Step-2: Let us put values of $x$ from $−2$ to $2$ into the function to obtain corresponding $y$ values. Using this we can plot a graph. Thus, For $x=−2$,$f(x)=−\frac{7}{2}=−3.5$ For $x=−1$, $f(x)=−\frac{13}{4}=−3.25$ For$x=0$, $f(x)=−3$ For$x=1$,$f(x)=−\frac{11}{4}=−2.75$ For$x=2$, $f(x)=−\frac{5}{2}=−2.5$ This data obtains the graph shown. Step-3: The average rate of change is defined as follows: $$\frac{Δy}{Δx}=\frac{f(x_2)−f(x_1)}{x_2−x_1}$$ Let us calculate the average rate of change between $x_2=2$ and $x_1=−2$, $$\frac{Δy}{Δx}=\frac{−2.5−(−3.5)}{2−(−2)}=\frac{1}{4}=0.25$$ Step-4: Since slope, $m=0.25>0$, this linear function is increasing.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.