How do you graph y-2<3x?

1 Answer
Jan 3, 2018

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]}