College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 1, Equations and Graphs - Section 1.3 - Lines - 1.3 Exercises: 22

Answer

$y=-\dfrac{4}{3}x-4$

Work Step by Step

RECALL: (1) The slope-intercept form of a line's equation is $y=mx+b$ where $m$ = slope and $b$ = y-intercept. (2) The slope of a line is equal to $\dfrac{rise}{run}$. Given two points on the line, rise is the increase (or decrease) in the y-value while run is the increase (or decrease) in the x-value. The line passes through the point $(0, -4)$ therefore the y-intercept is $-4$. The line also passes through the point $(-3, 0)$. Note that from $(-3, 0)$ to $(0, -4)$, there is a: decrease in y-value of 4 units $\longrightarrow \text{rise} = -4$ increase in x-value of 3 units $\longrightarrow \text{run} = 3$ Thus, the slope is: $=\dfrac{rise}{run} = \dfrac{-4}{3}=-\dfrac{4}{3}$ With $b=-4$ and $m=-\dfrac{4}{3}$, the equation of the line is: $y=mx + b \\y = -\dfrac{4}{3}x + (-4) \\y=-\dfrac{4}{3}x-4$
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