# How do you write an equation of a line passing through (1, -3), perpendicular to  y = 7x + 2?

Sep 3, 2016

The desired equation is
$x + 7 y + 20 = 0$

#### Explanation:

As the equation $y = 7 x + 2$ is already in slope intercept form, the slope is $7$.

Now, as the product of slopes of two perpendicular lines is $- 1$, the slope of line perpendicular to $y = 7 x + 2$ is $- \frac{1}{7}$.

Now the equation of a line passing through $\left({x}_{1} , {y}_{1}\right)$ and having a slope of $m$ is

$\left(y - {y}_{1}\right) = m \left(x - {x}_{1}\right)$

Hence equation of a line passing through $\left(1 , - 3\right)$ and having a slope of $- \frac{1}{7}$ id

y-(-3)=-1/7×(x-1) or

y+3=-1/7×(x-1) or

$7 y + 21 = - x + 1$ or

$x + 7 y + 20 = 0$