The inequalities are
y ≤ 2x + 1
and
y > -2x -3
Conveniently, they are already in slope-intercept form. Looking at the inequalities, we know off the bat there will be one dotted line and one solid line, since one is a "greater than" inequality (dotted line) and the other is "greater than or equal to" (solid line). This automatically rules our option B and C.
-The solid line will have a slope of 2 and a y-intercept of 1
-The dotted line will have a slope of -2 and a y-intercept of -3.
Both option A and D satisfy this, so which one has correct shading?
Option D has the shaded region below the solid line and above the dotted line, which agrees with our system of inequalities.
Answer is D
