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: 42


$\text{slope-intercept form: } y=-\dfrac{5}{6}x+\dfrac{31}{6} \\\\ \text{standard form: } 5x+6y=31$

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 $( -1,6 )$ and with a slope of $m= -\dfrac{5}{6} $ is \begin{array}{l}\require{cancel} y-6=-\dfrac{5}{6}(x-(-1)) \\\\ y-6=-\dfrac{5}{6}(x+1) .\end{array} In the form $y=mx+b$, the equation above is equivalent to \begin{array}{l}\require{cancel} y-6=-\dfrac{5}{6}(x+1) \\\\ y-6=-\dfrac{5}{6}x-\dfrac{5}{6} \\\\ y=-\dfrac{5}{6}x-\dfrac{5}{6}+6 \\\\ y=-\dfrac{5}{6}x-\dfrac{5}{6}+\dfrac{36}{6} \\\\ y=-\dfrac{5}{6}x+\dfrac{31}{6} .\end{array} In the form $Ax+By=C$, the equation above is equivalent to \begin{array}{l}\require{cancel} y=-\dfrac{5}{6}x+\dfrac{31}{6} \\\\ 6(y)=6\left( -\dfrac{5}{6}x+\dfrac{31}{6} \right) \\\\ 6y=-5x+31 \\\\ 5x+6y=31 .\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=-\dfrac{5}{6}x+\dfrac{31}{6} \\\\ \text{standard form: } 5x+6y=31 .\end{array}
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