Question

How do I write a linear inequality that represents the graph?

Answer 1

`y > -x+4`

Explanation:

we know that

The solution of the inequality is the shaded area above the dotted line

The slope of the dotted line is negative

The y-intercept of the dotted line is (0,4)

The x-intercept of the dotted line is (4,0)

Find the slope of the dotted line

`m=(0-4)/(4-0)\\ m=-1`

The equation of the dotted line in slope intercept form is equal to

`y=mx+b`

we have

`m=-1`

`b=4` -----> y-intercept

substitute

`y=-x+4`

Find the equation of the inequality

Remember that the solution is the shaded area above the dotted line therefore

The inequality is

`y > -x+4`