Explanation:
You graph linear inequalities the same way as the linear equations. Plot the given y-intercept, (0, 2), and use the slope, m = -3/4 (down 3, run 4) to plot other points. Make sure that you use a dashed line as your boundary, because of the inequality symbol, " > ."
In terms of shading, you must choose a test point (not within the line) to verify whether it will provide a true statement. If it does, then you would shade the region that contains that test point. If not, then you'll have to shade the half-plane region that doesn't contain that point. Usually, the point of origin, (0, 0) is used as a test point.
To demonstrate:
Substitute (0, 0) into the given inequality statement:
y > - ¾x + 2
0 > - ¾(0) + 2
0 > 0 + 2
0 > 2 (False statement). Therefore, you must shade the region that doesn't contain the point, (0, 0).