Question

How do you graph `y-2<3x`?

Answer 1

See a solution process below:

Explanation:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For: `x = 0`

`y - 2 = 3 xx 0`

`y - 2 = 0`

`y - 2 + color(red)(2) = 0 + color(red)(2)`

`y - 0 = 2`

`y = 2` or `(0, 2)`

For: `x = 1`

`y - 2 = 3 xx 1`

`y - 2 = 3`

`y - 2 + color(red)(2) = 3 + color(red)(2)`

`y - 0 = 5`

`y = 5` or `(1, 5)`

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

graph{(x^2+(y-2)^2-0.05)((x-1)^2+(y-5)^2-0.05)(y-3x-2)=0 [-16, 16, -8, 8]}

Now, we can shade the right side of the line. The boundary line will be dashed because the inequality operator does not contain an "or equal to" clause.

graph{(y-3x-2)<0 [-16, 16, -8, 8]}