Question

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 2) and (2, 0). Everything to the left of the line is shaded. The second dashed line has a negative slope and goes through (0, 2) and (4, 0). Everything below and to the left of the line is shaded.
Which system of linear inequalities is represented by the graph?

y > x – 2 and x – 2y < 4
y > x + 2 and x + 2y < 4
y > x – 2 and x + 2y < 4
y > x – 2 and x + 2y < –4

Answer 1

The system of linear inequalities that is represented by the graph is C. y > x – 2 and x + 2y < 4.

How to get the equation?

The first thing to to find the slope. This will be:

m = y2 - y1/x2 - x1

m = 0+2/2-0

m = 2

The equation in slope intercept form will be:

y = mx + b. The inequality will be y > x - 2.

Again, the slope will be:

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

= -1/2

The equation will be -1/2x + 2.

Multiply both sides by 2.

2y < -x + 4

x + 2t < 4

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