Question

How do you graph `y>x-4`?

Answer 1

See a solution process below:

Explanation:

First, change the inequality to an equality and solve for two points on the line:

For `x = 0`

`y = 0 - 4`

`y = -4` or `(0, -4)`

For `x = 4`

`y = 4 - 4`

`y = 0` or `(4, 0)`

We can now plot the two points on the grid.

graph{(x^2+(y+4)^2-0.05)((x-4)^2+y^2-0.05)=0 [-15, 15, -7.5, 7.5]}

We can now draw a line through these two points to create the inequality boundary. The line will be a dashed line because the inequality has just a "greater than" clause and does not have a "or equal to" clause. Therefore the line is not contained in the solution set.

We will also shade to the left of the line:

graph{y-x+4>0 [-15, 15, -7.5, 7.5]}