Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 1 - Linear Functions - 1.3 Fundamentals of Graphing and Slope - 1.3 Exercises: 34

Answer

$m=$$\frac{7}{4}$

Work Step by Step

To find the slope of the line that passes through the points in the table, use the slope formula: $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ Calculate the slope between each pair of points to find out if the slope is constant. The first pair of points is: (-3,14.25) and (0,9) Substitute: $m=\frac{9-14.25}{0-(-3)}=\frac{-5.25}{3}$ The second pair of points is: (0,9) and (3,3.75) Substitute: $m=\frac{3.75-9}{3-0}=\frac{-5.25}{3}$ The third pair of points is: (3,3.75) and (6,-1.5) Substitute: $m=\frac{-1.5-3.75}{6-3}=\frac{-5.25}{3}$ The slope is constant between each pair of points, so the slope of the line that passes through these points is $\frac{-5.25}{3}$. HOWEVER, decimals in a fraction make it confusing and messy. The best way to fix this is to find the smallest number to multiply the numerator by to make it whole. In this case, $-5.25$$\times$$4=-21$. Now, what is done to the numerator MUST be done to the denominator. So, $3$$\times$$4=12$. The new fraction $\frac{-21}{12}$=$\frac{-7}{4}$.
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.