Question

which of the following systems of inequalities matches the graph shown?
y ≤ -5x + 20 and y ≥ 2x - 4
y ≤ 5x - 5 and y ≥ x + 10
y ≤ -6x - 10 and y ≥ x + 9
y ≤ 6x - 7 and y ≥ x - 6

Explanation:

Step1: Find the y - intercept of the lines

The y - intercept is the value of y when x = 0. For the blue - shaded region line, when x = 0, y is around 20. For the red - shaded region line, when x = 0, y is around - 4.

Step2: Find the slope of the lines

The slope - intercept form of a line is y=mx + b, where m is the slope. For the blue - shaded region line, it has a negative slope. For the red - shaded region line, it has a positive slope.

Step3: Check the inequalities

The blue - shaded region is below its line, so it should be y≤mx + b. The red - shaded region is above its line, so it should be y≥mx + b.
For the line with negative slope, when x = 4, y = 0 in the blue - shaded region line. Using y=mx + b, 0=m×4 + 20, we get m=-5. For the line with positive slope, when x = 2, y = 0 in the red - shaded region line. Using y=mx + b, 0=m×2-4, we get m = 2.

Answer:

y≤ - 5x + 20 AND y≥2x - 4