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: 39

Answer

$y=3x-1$, or, in general form, $3x-y-1=0$

Work Step by Step

Through $(1,2);$ parallel to the line $y=3x-5$ Use the point-slope form of the equation of a line, which is $y-y_{1}=m(x-x_{1})$, where $(x_{1},y_{1})$ is a point through which the line passes and $m$ is the slope. $(x_{1},y_{1})$ and the equation of a line parallel to the line we have to find are given. Parallel lines have the same slope. The line given is written in slope-intercept form, so we can identify its slope as $3$ and this is also the slope of the line we have to find. Substitute $(x_{1},y_{1})$ and $m$ into the formula and simplify to obtain the equation of the line we have to find: $y-y_{1}=m(x-x_{1})$ $y-2=3(x-1)$ $y-2=3x-3$ $y=3x-3+2$ $y=3x-1$, or, in general form, $3x-y-1=0$
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