Question

How do you graph `y<3x-3/4` on the coordinate plane?

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 = (3 * 0) - 3/4`

2y = 0 - 3/4#

`y = -3/4` or `(0, -3/4)`

For: `x = 1`

`y = (3 * 1) - 3/4`

`y = 3 - 3/4`

`y = (4/4 * 3) - 3/4`

`y = 12/4 - 3/4`

`y = 9/4` or `(1, 9/4)`

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+(3/4))^2-0.035)((x-1)^2+(y-(9/4))^2-0.035)(y-3x+(3/4))=0 [-10, 10, -5, 5]}

Now, we can shade the right side of the line to represent the inequality.

The boundary line will be changed to a dashed line because the inequality operator does not contain an "or equal to" clause.

graph{(y-3x+(3/4)) < 0 [-10, 10, -5, 5]}