Question

How do you graph `x+2y >=-8` on a graphing calculator?

Answer 1

This depends on the capabilities of your calculator, however, converting the equation to a y=... format will work on many (if not all) graphing calculators.

Explanation:

first, lets start making the inequality a bit simpler for the calculator to understand by converting it to a function.

`x+2y=-8`

Then using basic algebra, we can move this to a calculators preferred form by solving for y.

`2y=-8-x`
`y=-(8/2)-(x/2)`
`y=-4-0.5x`

Once you plot this function, you can visualize the range of values where `y>=-4-0.5x`
These will be any point on the x,y plane that have a y-coordinate greater than that given by the function, creating a shaded area of infinite points vertically above the line.

For example, (2,1) will be in the shaded area above the line as the value of the function at x=2 (which is y=-5) will be less than the y-value associated with the point (2,1) (which is y=-1).