Question

How do you graph `2x-3y<6` 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`

`(2 * 0) - 3y = 6`

`0 - 3y = 6`

`-3y = 6`

`(-3y)/color(red)(-3) = 6/color(red)(-3)`

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

For: `y = 0`

`2x - (3 * 0) = 6`

`2x - 0 = 6`

`2x = 6`

`(2x)/color(red)(2) = 6/color(red)(2)`

`x = 3` or `(3, 0)`

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)^2-0.035)((x-3)^2+y^2-0.035)(2x-3y-6)=0 [-10, 10, -5, 5]}

Now, we can shade the left side of the line.

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

graph{(2x-3y-6) < 0 [-10, 10, -5, 5]}