Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 2 - Summary Exercises - Finding Slopes and Equations of Lines: 11

Answer

$\text{slope-intercept form: } y=-3x+10 \\\\ \text{standard form: } 3x+y=10$

Work Step by Step

Using $y-y_1=m(x-x_1)$ or the point-slope form of linear equations, the equation of the line passing through $( 4,-2 )$ and with a slope of $m= -3 $ is \begin{array}{l}\require{cancel} y-(-2)=-3(x-4) \\\\ y+2=-3(x-4) .\end{array} In the form $y=mx+b$, the equation above is equivalent to \begin{array}{l}\require{cancel} y+2=-3(x-4) \\\\ y+2=-3x+12 \\\\ y=-3x+12-2 \\\\ y=-3x+10 .\end{array} In the form $Ax+By=C$, the equation above is equivalent to \begin{array}{l}\require{cancel} y=-3x+10 \\\\ 3x+y=10 .\end{array} Hence, the different forms of the equation of the line with the given conditions are \begin{array}{l}\require{cancel} \text{slope-intercept form: } y=-3x+10 \\\\ \text{standard form: } 3x+y=10 .\end{array}
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