Question

Which is the graph of linear inequality x – 2y ≥ –12?

On a coordinate plane, a dashed straight line with positive slope goes through (negative 8, 2) and (0, 6). Everything to the right of the line is shaded.

On a coordinate plane, a solid straight line with positive slope goes through (negative 8, 2) and (0, 6). Everything to the left of the line is shaded.

On a coordinate plane, a dashed straight line with negative slope goes through (negative 6, 6) and (0, negative 6). Everything to the right of the line is shaded.

On a coordinate plane, a solid straight line with positive slope goes through (negative 8, 2) and (0, 6). Everything to the right of the line is shaded.

Answer 1

x - 2y ≥ -12
=> -2y ≥ -12 - x
=> y ≤ (x + 12)/2 = (1/2)x + 6.

Boundary: y = (1/2)x + 6, slope 1/2, passes through (-8,2) and (0,6); use a solid line (equality included). Test a point, e.g. (10,0): 10 - 0 ≥ -12 is true, so the half-plane on the right of that line is shaded.

So the correct choice is: "On a coordinate plane, a solid straight line with positive slope goes through (−8, 2) and (0, 6). Everything to the right of the line is shaded."