Question

Select the correct answer from each drop-down menu.

Which inequality is represented by the graph? Which test point holds true for the inequality?
1st drop down: 1. x + 3y is less than or equal to 8, 2. 4x + 3y is greater than or equal to 8, 3. 4x + 3y is less than or equal to 8, 4. 4x + 3y is less than or equal to 12.
2nd drop down: 1. (-1, 4), 2. (0, 3), 3. (1, 4), 4. (2, 1/3).

The graph represents the inequality . The test point holds true for this inequality.

Answer 1

The answer to you question is a) 3. 4x + 3y ≤ 8 b) (-1, 4)

Explanation:

Process

From the graph, get two points

A (-1, 4)

B (2, 0)

1.- Find the equation of the line

m = (4 - 0) / (-1 -2)

m = -4/3

y - 0 = -4/3(x - 2)

3(y - 0) = -4x + 8

3y - 0 = -4x +8

4x + 3y = 8

2.- Convert the line to an inequality

4x + 3y ≤ 8 Because we are interested in the area below the line.

Second part

The only point that satisfies the inequality is (-1, 4)