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

Nov 28, 2017

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.

$a - b \ge 6$
$a \ge 6 + b$
$a - 6 \ge b$
$b \le a - 6$

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 $\left(5 , 5\right)$.

$\left(5\right) - 5 \left(5\right) \ge 6$
$0 \ge 6$ which is absurd (slightly), so we know the other region is the 'correct' one. You may wish to check the points$\left(5 , - 5\right) , \left(0 , 0\right) , \left(15 , 2\right)$ or $\left(7 , - 1\right)$ 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 $a - b \ge 6$ You should also label the line as $a - b > 6$