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: 47

Answer

(a) slope = $\frac{-1}{3}$. y-intercept: $(0, 2)$ x-intercept: $(6, 0)$ (b) $y=-\frac{1}{3}x+2$.

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 $(0, 2)$ to the point $(3, 1)$, the change in $y$ is $-1$ while the change in $x$ is $3$. Thus, the slope is $\frac{-1}{3}$. The graph crosses the y-axis at the y-intercept $(0, 2)$. With a slope of $-\frac{1}{3}$, for a change of $3$ units in $x$, there corresponds a 1-unit decrease in the value of $y$. Thus, from $(3, 1)$, a 3-unit increase in $x$ gives a 1-unit decrease in $y$ leading to the x-intercept of $(6, 0)$ (b) With a slope of $-\frac{1}{3}$ and a y-intercept of $(0, 2)$, then the equation of the line is $y=-\frac{1}{3}x+2$.
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