Question

(04.06 MC) In the graph, the area below 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. Graph of two intersecting lines. One line f of x is solid and goes through the points 0, 4, and 4, 0 and is shaded above the line. The other line g of x is solid, and goes through the points 0, negative 1 and 2, 5 and is shaded in below the line. The graph represents which system of inequalities? y ≤ −3x − 1 y ≤ −x − 4 y ≥ −3x + 1 y ≤ −x − 4 y ≤ 3x − 1 y ≤ −x + 4 y ≤ 3x − 1 y ≥ −x + 4

Answer 1

Answer:

(D)y ≤ 3x − 1 y ≥ −x + 4

Step-by-step explanation:

The line f(x) is solid and goes through the points (0, 4) and (4, 0) and is shaded above the line.

The line that satisfies the point (0,4) and (4,0) is y=-x+4

Since it is shaded above the line, we have the inequality sign  ≥.

Therefore, one of the lines is y≥-x+4

In the equation of the line y=3x-1

When x=0, y=3(0)-1=-1

When x=2, y=3(2)-1=5

Since it is shaded below the line, we have the inequality sign ≤ .

Therefore, the other line is y≤3x-1.

The correct option is D.