## Intermediate Algebra (12th Edition)

$\text{slope-intercept form: } y=x-2 \\\\ \text{standard form: } x-y=2$
Using $y-y_1=m(x-x_1)$ or the point-slope form of linear equations, the equation of the line passing through $( 12,10 )$ and with a slope of $m= 1$ is \begin{array}{l}\require{cancel} y-10=1(x-12) .\end{array} In the form $y=mx+b$, the equation above is equivalent to \begin{array}{l}\require{cancel} y-10=1(x-12) \\\\ y-10=x-12 \\\\ y=x-12+10 \\\\ y=x-2 .\end{array} In the form $Ax+By=C$, the equation above is equivalent to \begin{array}{l}\require{cancel} y=x-2 \\\\ -x+y=-2 \\\\ x-y=2 .\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=x-2 \\\\ \text{standard form: } x-y=2 .\end{array}