Question

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

Answer 1

Refer to the explanaation.

Explanation:

Graph:

`-3x+2y<2` is a linear equation in standard form.

To graph a linear equation/inequality, you need a minimum of two points. I prefer to use the x- and y-intercepts.

X-intercept: value of `x` when `y=0`

Substitute `0` for `y`. Set the two sides equal to one another.

`-3x+2(0)=2`

Simplify.

`-3x=2`

Divide both sides by `-3`. This will reverse the inequality.

`x=-2/3`

x-intercept: `(-2/3,0)`

Y-intercept: value of `y` when `x=0`

Substitute `0` for `x`. Set the two sides equal to one another.

`-3(0)+2y=2`

Simplify.

`2y=2`

Divide both sides by `2`.

`y=1`

x-intercept: `(0,1)`

Plot the points for the x- and y-intercepts. Draw a dashed straight line through the points to show that the line is the boundary of the inequality, but is not part of it. Shade the area beneath the line to represent the "less than" inequality.

graph{-3x+2y<2 [-10, 10, -5, 5]}