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: 19

Answer

$y=-x + 4$

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 $(1, 3)$. Note that from $(0, 4)$ to $(1, 3)$, there is a: decrease in y-value of 1 unit $\longrightarrow \text{rise} = -1$ increase in x-value of 1 unit $\longrightarrow \text{run} = 1$ Thus, the slope is: $=\dfrac{rise}{run} = \dfrac{-1}{1} = -1$ With $b=4$ and $m=-1$, the equation of the line is: $y=mx + b \\y = -1(x) + 4 \\y=-x + 4$
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