Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.4 - Linear Functions and Slope - Exercise Set - Page 215: 91


The linear function obtained is $f\left( x \right)=-2.36x+254.84$.

Work Step by Step

Locate any two points in the line and use them to calculate the slope of the linear function as follows: The two points of the line are $\left( {{x}_{1}},{{y}_{1}} \right)=\left( 19,210 \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)=\left( 74,80 \right)$. Obtain the value of slope (m) using the formula given below: $\begin{align} & m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\ & =\frac{80-210}{74-19} \\ & =-2.36 \end{align}$ Now, substitute the slope in the line equation as follows: $\begin{align} & \left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right) \\ & \left( y-210 \right)=-2.36\left( x-19 \right) \\ & \left( y-210 \right)=-2.36x+44.84 \\ & y+2.36x=254.84 \end{align}$ So, the function obtained is $f\left( x \right)=-2.36x+254.84$. The slope of the function is defined as the change in y per unit change in the x coordinate. That means that for every unit change in $x$, $y$ decreases by $2.36$ units. Here, $y$ is the child mortality rate (children aged under 5) and $x$ is the percentage of female adults who are literate. So, for every $1$ unit percentage increase of literacy in women, the child mortality decreases by 2.36. Hence, the function of the given data is $f\left( x \right)=-2.36x+254.84$ and for every $1$ unit percentage increase of literacy in woman, the child mortality decreases by 2.36.
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