Question

How do you graph the inequality `x + y <5`?

Answer 1

Draw a dotted line connecting (0,5) and (5,0).
Shade the area under the line.

Explanation:

Find the two intercepts on the axes first...
To do this, use `x+y = 5`

For the x-intercept, make y = 0
`x = 5`

For the y-intercept, make x = 0
`y = 5`

Plot these two points on the axes and connect them with a dotted line because we are working with an inequality and the line itself is NOT included in the solution.

The required solution is the area of the Cartesian plane where the sum of any x- and y- values is less than 5.

The required area is that part BELOW the line.

Check by choosing the origin. (0,0)

`0 + 0 = 0` which is a possible solution, so this point lies in the required area.

Shade under the line as the answer.