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 - Page 173: 48


$\text{slope-intercept form: } y=0.8x-6 \\\\ \text{standard form: } 4x-5y=30$

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 $( 6,-1.2 )$ and with a slope of $m= 0.8 $ is \begin{array}{l}\require{cancel} y-(-1.2)=0.8(x-6) \\\\ y+1.2=0.8(x-6) .\end{array} In the form $y=mx+b$, the equation above is equivalent to \begin{array}{l}\require{cancel} y+1.2=0.8x-4.8 \\\\ y=0.8x-4.8-1.2 \\\\ y=0.8x-6 .\end{array} In the form $Ax+By=C$, the equation above is equivalent to \begin{array}{l}\require{cancel} y=0.8x-6 \\\\ 10(y)=(0.8x-6)10 \\\\ 10y=8x-60 \\\\ -8x+10y=-60 \\\\ 8x-10y=60 \\\\ \dfrac{8x-10y}{2}=\dfrac{60}{2} \\\\ 4x-5y=30 .\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=0.8x-6 \\\\ \text{standard form: } 4x-5y=30 .\end{array}
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