Question

How do you graph the inequality `y<= 2x + 2`?

Answer 1

See the explanation.

Explanation:

Suppose `x=3` then `2x+2=8`

So the inequality of `y<=2x+2` for `x=3` is saying:

`y` can be 8 and/or all the values less than 8

As `y` can actually assume the value of 8 the line is solid.

Suppose the equation had been `y<2x+2` in this instance if `x=3` then `y` is not permitted to assume the value of 8 but it is allowed to assume any of the values less than 8. In this case the line would be dotted.

Answer 2

Draw the line `y=2x+2` that passes through `(-1, 0 and (0, 2)`. Shade the region below. For any (x, y) on and beneath this line `y<=2x+2`.

Explanation:

Draw the line `y=2x+2`. It passes through `(-1, 0 and (0, 2)`. Shade

the region below this line.

For any point (x, y) on and beneath this linem `y<=2x+2`.