# Are the graph  y=x and y=3 perpendicular?

May 7, 2016

No. $y = x$ has a gradient of 1.
$y = 3$ is a horizontal line, ie the gradient = 0.
These two lines meet at an angle of 45°

#### Explanation:

Consider $y = x \mathmr{and} y = x$ in the form $y = m x + c$

$y = 1 x + 0$ The slope = 1. It is a diagonal line and a line of symmetry of the cartesian plane. It lies at an inclination of 45°.

$y = 0 x + 3$ has a gradient of 0.

A vertical line would be perpendicular to a horizontal line - a line with an infinite (undefined) gradient and a line with a zero gradient meet at 90°.