Question

Graph the inequality below.
y > −x + 2


-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
9
8
7
6
5
4
3
2
1
-1
-2
-3
-4
-5
-6
-7
-8
-9
x

Answer 1

To graph y > −x + 2:

1. Graph the boundary line y = −x + 2.
- It has y-intercept (0, 2) and x-intercept (2, 0).
- Slope = −1, so from (0,2) go right 1 and down 1 to get other points.
- Draw this line as a dashed (not solid) line because the inequality is strict (>), so points on the line are not included.

2. Shade the half-plane above the line.
- Pick a test point not on the line, e.g. (0,3): 3 > −0 + 2 → 3 > 2 is true, so the region containing (0,3) is the solution region.
- The origin (0,0) gives 0 > 2 (false), so do not shade the side containing the origin.

Result: the graph is the dashed line through (0,2) and (2,0) with the region above that line shaded.