Question

The graph below shows the solution to a system of inequalities: Solid line joining ordered pairs 0, 3.75 and 15, 0. Shade the portion of the graph above the line in the first and second quadrant Which of the following inequalities is modeled by the graph? (5 points) Group of answer choices x + 4y ≥ 15; y ≥ 0 x − 4y ≥ 15; y ≥ 0 x + 4y ≤ 15; y ≥ 0 −x − 4y ≥ 15; y ≥ 0

Answer 1

Answer: He right

Explanation:

Answer 2

x + 4y ≥ 15; y ≥ 0

Explanation:

The solid line signifies it is a ≤ or ≥.

The equation of the line joining 0, 3.75 and 15, 0 is gotten using the formula:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)\\\\Substituting:\\\\y-3.75=(0-3.75)/(15-0)(x-0)\\\\ y-3.75=-(1)/(4)x\\\\y=-(1)/(4)x+3.75\\\\4y=-x+15\\\\4y+x=15`

Since the first and second quadrant are shaded, this represents y ≥ 0.

Also, above the solid line of 4y + x = 15 is shaded, this represents 4y + x ≥ 15.

Hence the inequality modeled is x + 4y ≥ 15; y ≥ 0