# What is the basic difference between the lines y = x and y = -x?

Mar 23, 2018

See explanation

#### Explanation:

Consider $y = x$

The count of $x ' s$ is 1 so although it is not normally shown we actually have $y = + 1 x$

This number 1 is the slope (gradient) which is the amount of up or down for 1 along reading left to right on the x-axis.

As the vertical position increases (positive direction) the slope is upwards

Consider $y = - x \to y = - 1 x$

In this case the the vertical position decreases (negative direction) the slop is downwards.