Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.10 - Lines - 1.10 Exercises - Page 115: 85

Answer

(a) See prove below. (b) $4x-3y-24=0$

Work Step by Step

(a) Given the x-intercept as $a$ and the y-intercept as $b$, we have two points on the line as $(a,0)$ and $(0,b)$, the slope of the line is then given by $m=\frac{b-0}{0-a}=-\frac{b}{a}$. Thus, the equation of the line can then be written as $y=-\frac{b}{a}x+b$ which gives $\frac{b}{a}x+y=b$, divide $b$ on both sides, we get $\frac{x}{a}+\frac{y}{b}=1$ which proves the formula. (b) Given $a=6,b=-8$, the equation becomes $\frac{x}{6}-\frac{y}{8}=1$, multiply 24 on both sides and rearrange the equation to get $4x-3y-24=0$
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