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: 45

Answer

(a) slope = $-2$ y-intercept: $(0, 1)$ x-intercept is $(0.5, 0)$ (b) $y=-2x+1$

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 $((0, 1)$ to the point $(1, -1)$, the change is $y$ is $-2$ while the change in $x$ is $1$. Thus, the slope is $\frac{-2}{1}=-2$. The graph crosses the y-axis at the y-intercept $(0, 1)$. With a slope of $-2$, for a change of $0.5$ in $x$, there corresponds a 1-unit decrease in the value of $y$. Thus, the x-intercept is $(0.5, 0)$ (b) With a slope of $-2$ and a y-intercept of $(0, 1)$, then the equation of the line is $y=-2x+1$.
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