College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

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

Answer

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.
1510414088

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.
Small 1510414088
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

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.