Region A: y ≥ x-6
Region B: y ≤ x-6
Since its a solid line, the inequality symbol will be ≤ or ≥.
so, y ≤ mx+b would be the formula for region B because the shaded region is going down
and y ≥ mx+b would be for region A because the shaded region is going up
First, we need to find m, slope.
slope formula: y2-y1/x2-x1
1st point: (2,-4)
2nd point: (3,-3)
y2-y1/x2-x1 ---> -3 + 4 / 3 - 2
Simplify.
-3 + 4 / 3 - 2 ----> 1 / 1
1 / 1 = 1
So m = 1
Since the regions share the same line, the slope for both will be the same.
Now we need b, y-intercept. (-6)
Fill in the formula for both regions.
Region A: y ≥ mx+b
y ≥ 1x-6
(cancel the 1)
y ≥ x-6
Region B: y ≤ mx+b
y ≤ 1x-6
(cancel the 1)
y ≤ x-6
Let me know if you have any questions :)