Intermediate Algebra (12th Edition)

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

Chapter 2 - Section 2.3 - Writing Equations of Lines - 2.3 Exercises: 47

Answer

$7x-5y=-20$

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 $( 2,6.8 )$ and with a slope of $m= 1.4 $ is \begin{array}{l}\require{cancel} y-6.8=1.4(x-2) .\end{array} In the form $y=mx+b$, the equation above is equivalent to \begin{array}{l}\require{cancel} y-6.8=1.4x-2.8 \\\\ y=1.4x-2.8+6.8 \\\\ y=1.4x+4 .\end{array} In the form $Ax+By=C$, the equation above is equivalent to \begin{array}{l}\require{cancel} y=1.4x+4 \\\\ -1.4x+y=4 \\\\ 1.4x-y=-4 \\\\ 10(1.4x-y)=(-4)10 \\\\ 14x-10y=-40 \\\\ \dfrac{14x-10y}{2}=\dfrac{-40}{2} \\\\ 7x-5y=-20 .\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=1.4x+4 \\\\ \text{standard form: } 7x-5y=-20 .\end{array}
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