# How do you write the equation of a line in slope intercept form that is parallel to the line y=1/3x+5 and passes through (-9, 5)?

May 8, 2016

$y = - 3 x - 22$

#### Explanation:

If you have the slope of a line, $m$ and one point, $\left({x}_{1} , {y}_{1}\right)$ the easiest way to find its equation is by using the formula: $y - {y}_{1} = m \left(x - {x}_{1}\right)$

Let's find the slope first. If two lines are perpendicular, then the one slope is the negative reciprocal of the other.. ie ${m}_{1} \times {m}_{2} = - 1$

The line we want to know about is perpendicular to a line with a slope of $\frac{1}{3}$, so the new slope is -3. We have the point $\left(- 9 , 5\right)$

Substitute into $y - {y}_{1} = m \left(x - {x}_{1}\right)$ and simplify
$y - 5 = - 3 \left(x - \left(- 9\right)\right) \Rightarrow y - 5 = - 3 \left(x + 9\right)$

$y = - 3 x - 27 + 5$

$y = - 3 x - 22$