Question

How do you graph the inequality `2y - 3x >6`?

Answer 1

Draw the line then shade where it is true. See below.

Explanation:

Strategy: Figure out what the line would look like using `2y-3x=6`. Then, plugging in a few choice points, find `x` and `y` values that, when plugged in, are truly greater than `6`. Shade the side where the inequality is true.

Step 1. Graph the line `2y-3x=6`

Rewrite this equation with `y` on one side alone.
`2y=3x+6`
`y=3/2x+3`

Slope: `m=3/2`, that is a rise of 3 and run of 2
`y`-intercept: `(0, 3)`

graph{y=3/2x+3}

Step 2. Find some points where `x` and `y` will make the inequality true.

Try the point `(0,0)`:
`2(0)-3(0)>6` or `0>6` is FALSE. Do not shade this side of the line.

Try the point `(-5,0)`:
`2(0)-3(-5)>6` or `15>6` is TRUE. So, do shade this side of the line.

Because the inequality is `>`, use a dashed line.

graph{2y-3x>6}