Question

On a coordinate plane, a solid straight line has a negative slope and goes through (negative 2, 2) and (2, negative 8). Everything above and to the right of the line is shaded. The line has an equation of y greater-than-or-equal-to negative five-halves x minus 3.
Which linear equality will not have a shared solution set with the graphed linear inequality?

y > Two-fifthsx + 2
y < Negative five-halvesx – 7
y > Negative two-fifthsx – 5
y < Five-halvesx + 2

Answer 1

y < -5/2 x - 7

Reason: the graphed region is y ≥ -5/2 x - 3. For every x,
-5/2 x - 3 ≥ -5/2 x - 7,
so no y can satisfy y ≥ -5/2 x - 3 and y < -5/2 x - 7 at the same time.