Question

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

Answer 1

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 and y = x` in the form `y = mx + c`

`y = 1x + 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 = 0x + 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°.