# How do you solve the system y=1/3x and y=1/3x-2 by graphing?

Jul 26, 2018

The solution is $S = \emptyset$

#### Explanation:

Start by plotting

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

graph{1/3x [-10, 10, -5, 5]}

This is a straight line passing through the origin.

Then on the same graph, plot

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

graph{(y-1/3x)(y-1/3x+2)=0 [-10, 10, -5, 5]}

The graph are parallel, therefore, no solutions

We could have reached the same conclusions, as the gradients of the $2$ lines are identical.

Gradient is $m = \frac{1}{3}$