Question

In the graph, the area above f(x) is shaded and labeled A, the area below g(x) is shaded and labeled B, and the area where f(x) and g(x) have shading in common is labeled AB.

(insert photo from below)

The graph represents which system of inequalities?
A: y > 2x − 3 y > −x − 3
B: y < 2x − 2 y < −x + 3
C: y ≤ 2x − 2 y > −x + 3
D: None of the above

Answer 1

C: y ≤ 2x − 2 y > −x + 3

Explanation:

the symbol ≤ will give you a solid line

Answer 2

C: y ≤ 2x − 2 y > −x + 3

Explanation:

The shading for region A is above a dashed line with negative slope, so will be the solution of an inequality that matches y > -ax +b. Choices A and C have such an inequality.

The shading for region B is below a solid line with positive slope, so will be the solution of an inequality that matches y ≤ ax +b (for some positive a). Choice C is the only one wht the appropriate inequality symbol.

Comparing choice C in detail with the graph, we find that it matches. The line with negative slope has a slope of -1 and a y-intercept of 3, so region A matches y > -x+3. The line with positive slope has a slope of +2 and a y-intercept of -2, so region B matches y ≤ 2x -2.