Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 2 - Section 2.5 - Linear Functions and Models - 2.5 Exercises - Page 196: 35

Answer

a. Rate of change = $-\frac{1}{2}$ b. $f(x) = -\frac{1}{2} + 2$

Work Step by Step

a. The rate of change is how much $y$-increases for every increase in the $x$ value. Use the slope formula: $\text{Slope}=\dfrac{y_{2}-y_{1}}{x_{2}-x_{2}}$. Pick two points from the graph and plug them into the formula, for example $(4,0)$ and $(0,2)$ to get the slope, which is also the rate of change: $\text{Slope}=\dfrac{2-0}{0-4}=-\dfrac{2}{4}=-\dfrac{1}{2}$. b. The rate of change is $a$ and the $y$-intercept is $b$. The $y$-intercept occurs when $x = 0$, which means that, based off the graph given, $b= 2$. So the overall equation for the function is $f(x) = -\dfrac{1}{2}x + 2$
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