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: 15

Answer

(a) Slope $= -3$ and y-intercept $=4$ (b) See the image. (c) Average rate of change $= -3$ (d) The linear function $h(x)=-3x+4$ is decreasing.
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Work Step by Step

Step-1: Compare the given equation with the point-slope form of the linear equation, that is, $h(x) = mx+b$, where $m$ is the slope of the linear function and $b$ is its y-intercept. By comparing $$h(x)=-3x+4$$ to $$h(x) = mx+b$$ we that understand that the slope of the given function is $-3$ and its y-intercept is $4$. 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 $x=-2$, $h(x)=10$ For $x=-1$, $h(x)=7$ For $x=0$, $h(x)=4$ For $x=1$, $h(x)=1$ For $x=2$, $h(x) = -2$ This data obtains the graph shown. Step-3: The average rate of change is defined as follows: $$\frac{\Delta y}{\Delta x}=\frac{h(x_2)-h(x_1)}{x_2-x_1}$$ Let us calculate average rate of change between $x_2=2$ and $x_1=-2$, $$\frac{\Delta y}{\Delta x}=\frac{-2-10}{2-(-2)}=-3$$ Step-4: Since slope, $m=-3<0$, this linear function is decreasing.
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