Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 2 - Graphs and Functions - 2.4 Linear Functions - 2.4 Exercises - Page 229: 54


(a) slope = $-\frac{5}{4}$ (b) Refer to the graph below.

Work Step by Step

Solve for $y$ by dividing both sides of the equation by $-4$: $\frac{-4y}{-4}=\frac{5x}{-4} \\y = -\frac{5}{4}x$ This means the given equation is equivalent to $y=-\frac{5}{4}x$. RECALL: In the linear equation $y=mx + b$, $m$=slope and $(0, b)$ is the y-intercept. (a) The line $y=-\frac{5}{4}x$ has a slope of $-\frac{5}{4}$ and a y-intercept of $(0, 0)$. (b) To graph the line, perform the following steps: (1) Plot the y-intercept $(0, 0)$. (2) Use the slope to plot another point. The slope is $-\frac{5}{4}=\frac{-5}{4}$ so there is a 5-unit decrease in the value of $y$ for every 4-unit increase in $x$. From $(0, 0)$, move 5 units down (the rise) and 4 units to the right (the run) to reach $(4, -5)$. Plot $(4, -5)$. (3) Complete the graph by connecting the two points using a line. (Refer to the graph in the answer part above.)
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