# Chapter 2 - Section 2.3 - Writing Equations of Lines - 2.3 Exercises - Page 173: 71

$\text{slope-intercept form: } y=3x-19 \\\\ \text{standard form: } 3x-y=19$

#### Work Step by Step

In the slope-intercept form, the given equation, $3x-y=8 ,$ is equivalent to \begin{array}{l}\require{cancel} -y=-3x+8 \\\\ y=3x-8 .\end{array} Hence, the slope of this line is $3 .$ Since the line passing through the given point, $( 7,2 ),$ is parallel to the previous line, then the slopes of these lines are equal. Using $y-y_1=m(x-x_1)$ or the point-slope form, the equation of the line is \begin{array}{l}\require{cancel} y-2=3(x-7) .\end{array} In $y=mx+b$ form, the equation above is equivalent to \begin{array}{l}\require{cancel} y-2=3x-21 \\\\ y=3x-21+2 \\\\ y=3x-19 .\end{array} In $Ax+By=C$ form, the equation above is equivalent to \begin{array}{l}\require{cancel} -3x+y=-19 \\\\ 3x-y=19 .\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-19 \\\\ \text{standard form: } 3x-y=19 .\end{array}

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