# How do you find equations of the lines passing through (1,3 ) perpendicular to line x+y=0?

Jun 17, 2016

$y = x + 2$

#### Explanation:

There will only be one line which meet these conditions.

$x + y = 0 \Rightarrow y = - x$
This line has a gradient = -1.
The line perpendicular to it has a gradient of 1.
$\text{ } {m}_{1} \times {m}_{2} = - 1$

We have (x,y) = (1,3) and m = 1

$y = m x + c$ becomes $3 = 1 \left(1\right) + c$

$3 = 1 + c \Rightarrow c = 2$

Equation is $y = x + 2$