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 - 1.4 Intercepts and Graphing - 1.4 Exercises - Page 63: 39


Refer to th graph below.

Work Step by Step

Recall: The line $y=m x+b$ has a slope of $m$ and a $y$-intercept of $(0, b)$. Thus, the given line has $(0, -6)$ as $y$-intercept. Find the $x$-intercept by setting $y=0$ then solving for $x$ to obtain: \begin{align*} \require{cancel} y&=\frac{3}{7}x-6\\ 0&=\frac{3}{7}x-6\\ 6&=\frac{3}{7}x\\ \frac{7}{3} \cdot 6 &= \frac{3}{7}x \cdot \frac{7}{3}\\ \frac{7}{\cancel{3}} \cdot \cancel{6}^2 &= \cancel{\frac{3}{7}}x \cdot \cancel{\frac{7}{3}}\\ 14&=x \end{align*} Thus, the $x$-intercept is at $(14, 0)$. Plot the $x$ and $y$-intercepts then connect them using a straight line. Refer to the graph above.
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