Question

0147:03

Which system of linear inequalities is represented by
the graph?
O y2X-2 and x - 2y <4
O y2 x + 2 and x + 2y <4
O y> x-2 and x + 2y < 4
O y>X-2 and x + 2y <-4

Answer 1

y ≥ x - 2 and x + 2y < 4

Explanation:

There are two lines graphed.

The dotted line passes through (0,2) and (4,0), then:

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

y-intercept (b): 2

equation:

y = mx + b

y = -1/2x + 2

multiplying by 2 at both sides, we get

2y = -x + 4

x + 2y = 4

The inequality is x + 2y < 4 because points below this line are shaded and points on the line are not included.

The solid line passes through (0,-2) and (2,0), then:

slope (m): (0 - (-2))/(2 - 0) = 1

y-intercept (b): -2

equation:

y = x - 2

The inequality is y ≥ x - 2 because points above this line are shaded and points on the line are included.