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

Aug 27, 2016

$y = \frac{1}{3} x + 2$

#### Explanation:

The gradient of $y = - 3 x + 7$ is -3
The gradient of a line perpendicular is $\frac{1}{3}$
To prove this to yourself draw a line with gradient -3 on squared paper and the draw a line at right angles

So the line of the perpendicular will be in the form
$y = \frac{1}{3} x + c$
But we know it goes through (-3,1)
So substituting those values gives
$1 = \frac{1}{3} \cdot - 3 + c$
1=-1+c
c=2