# Equation in slope intercept form. line f has an equation of y=-9/10x-7 line g in

Equation in slope intercept form. line f has an equation of y=-9/10x-7 line g includes the point (-3,-5)and is perpendicular to line f. What is the equation of line g?
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Step 1
Given, line f has an equation of $y=-\frac{9}{10}x-7$
$\therefore$ Slope of line f, ${m}_{1}=-\left(\frac{9}{10}\right)$
Step 2
Line g is perpendicular to line f
$\therefore$ Slope of line g, ${m}_{2}=-\left(-\frac{1}{\frac{9}{10}}\right)=\frac{10}{9}$
line g includes the point (-3,-5)
$\therefore$ equation of line g:
$\left(y-\left(-5\right)\right)=\left(\frac{10}{9}\right)\left(x-\left(-3\right)\right)$
$⇒\left(y+5\right)=\left(\frac{10}{9}\right)\left(x+3\right)$