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: 41

Answer

$3x+4y=10$

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 $( -2,4 )$ and with a slope of $m= -\dfrac{3}{4} $ is \begin{array}{l}\require{cancel} y-4=-\dfrac{3}{4}(x-(-2)) \\\\ y-4=-\dfrac{3}{4}(x+2) .\end{array} In the form $y=mx+b$, the equation above is equivalent to \begin{array}{l}\require{cancel} y-4=-\dfrac{3}{4}(x+2) \\\\ y-4=-\dfrac{3}{4}x-\dfrac{3}{2} \\\\ y=-\dfrac{3}{4}x-\dfrac{3}{2}+4 \\\\ y=-\dfrac{3}{4}x-\dfrac{3}{2}+\dfrac{8}{2} \\\\ y=-\dfrac{3}{4}x+\dfrac{5}{2} .\end{array} In the form $Ax+By=C$, the equation above is equivalent to \begin{array}{l}\require{cancel} y=-\dfrac{3}{4}x+\dfrac{5}{2} \\\\ 4(y)=4\left(-\dfrac{3}{4}x+\dfrac{5}{2}\right) \\\\ 4y=-3x+10 \\\\ 3x+4y=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=-\dfrac{3}{4}x+\dfrac{5}{2} \\\\ \text{standard form: } 3x+4y=10 .\end{array}
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