Precalculus (6th Edition)

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

Chapter 2 - Graphs and Functions - 2.5 Equations of Lines and Linear Models - 2.5 Exercises - Page 244: 49


(a) slope =$-200$. y-intercept: $(0, 300)$ x-intercept: $(1.5, 0)$ (b) $y=-200x+300$

Work Step by Step

RECALL: (1) The slope is the ratio rise (change in y) over run (change in x). (2) The x-intercept is the point where the graph touches/crosses the x-axis. (3) The y-intercept is the point where the graph touches/crosses the y-axis. (4) The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $(0, b)$ is the line's y-intercept. (a) From the point $(0, 300)$ to the point $(1, 100)$, the change in $y$ is $-200$ while the change in $x$ is $1$. Thus, the slope is $\frac{-200}{1}=-200$. The graph crosses the y-axis at the y-intercept $(0, 300)$. With a slope of $-200$, from $(1, 100)$, a change of $0.5$ unit in the value of $x$ gives a $-100$ unit decrease in $y$, leading to the x-intercept $(1.5, 0)$. (b) With a slope of $-200$ and a y-intercept of $(0, 300)$, then the equation of the line is $y=-200x+300$.
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