Question

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

Answer 1

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.