Question

Please help me to write a linear inequality that represents the graph

Answer 1

`y>4-x`

Explanation:

First, see at dotted line. This line passes through the points (4,0) and (0,4). Then the equation of this line is

`(x-4)/(0-4)=(y-0)/(4-0)\\ \\(x-4)/(-4)=(y)/(4)\\ \\x-4=-y\\ \\y=4-x`

This line divides the coordinate plane into two regions where
`y<4-x` and
`y>4-x`. The origin does not belong to the shaded region, so its coordinates does not satisfy the inequality. Check

`0<4-0\\ \\0<4,`

then the origin belongs to the region with inequality
`y<4-x.`

Then the needed inequality is
`y>4-x.`

Note that sign is without notion "or equal to", because the line is dotted.