Question

How do you graph the inequality `a - b >= 6`?

Answer 1

Rearrange to having one variable as the subject. and plot with a dotted line.

Explanation:

Perhaps some confusion regarding graphing this is which variable goes on which axis. I will let a be the x-axis, and b the y-axis (this is marginally more challenging than the other way round).

First, we want to rearrange to make b the subject.

`a-b>=6`
`a>=6+b`
`a-6>=b`
`b<=a-6`

To plot this on a graph, we first want to draw on the line `b=a-6`

graph{x-y=6 [-14.08, 17.94, -7.5, 8.52]}

And now, we denote the region which satisfies this inequality. Since our inequality is less than, the region below the line satisfies the inequality. If you aren't 100% sure whether you have the right region, take a point and check.
Eg:
If I thought it was above the line, I might check the point `(5,5)`.

`(5)-5(5)>=6`
`0>=6` which is absurd (slightly), so we know the other region is the 'correct' one. You may wish to check the points`(5,-5), (0,0), (15,2)` or `(7,-1)` as some examples, as an exercise.

Now, we denote our region:

graph{x-y>=6 [-22.94, 34.77, -11.97, 16.9]}

This graph has done this by shading. You may alternatively want to draw an R in the region, and leave a key saying the R is the region for which `a-b>=6` You should also label the line as `a-b>6`