# How do you graph y <x and x>5 on the axes below?

Sep 30, 2017

See below.

#### Explanation:

First plot the line $y = x$. This will give you one of the boundary lines. Remember to use a dashed line as this is a less than inequality and not a less than or equal to inequality.

Plot the line $x = 5$. This will give you another boundary line. As before use a dashed line, because this is a greater than and not a greater than or equal to.

Test values on either side of each line to determine what region is shaded.

For $y < x$, if $x = 4$, $y < x$ below the line $y = x$

For $x > 5$ , if $x = 6$, to right of line $x = 5$

To satisfy both conditions.

$x > 5$ and $y < x$

if $x = 6$ and $y = 2$

This is the region below the line $y = x$ and to the right of the line $x = 5$. This is shown as the grey region on the graph.

Graph of $y < x , x > 5$:

This can seem a bit confusing. It is generally best practice in a case like this to plot the line of each inequality and determine the regions by examining the graph.