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: 48

Answer

(a) slope is $\frac{3}{4}$ y-intercept: $(0, -3)$ x-intercept $(4, 0)$ (b) $y=\frac{3}{4}x-3$

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 $(0, -3)$ to the point $(4, 0)$, the change in $y$ is $3$ while the change in $x$ is $4$. Thus, the slope is $\frac{3}{4}$. The graph crosses the y-axis at the y-intercept $(0, -3)$. The graph crosses the x-axis at the x-intercept $(4, 0)$. (b) With a slope of $\frac{3}{4}$ and a y-intercept of $(0, -3)$, then the equation of the line is $y=\frac{3}{4}x-3$.
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