Question

Graph the inequality on the axes below.
y, is greater than, one half, x, minus, 2
y>1/2x−2 on a grap with two points

Answer 1

Step 1 — draw the boundary line y = (1/2)x − 2 as a dashed line (use dashed because the inequality is strict, “>”, so the line is NOT included).

Step 2 — plot two points on that line:
- x = 0 → y = (1/2)(0) − 2 = −2 → point (0, −2)
- x = 2 → y = (1/2)(2) − 2 = 1 − 2 = −1 → point (2, −1)
(You could also use x = 4 → y = 0 → point (4, 0).)

Connect the points with a dashed straight line. The slope is 1/2 (rise 1, run 2).

Step 3 — decide which side to shade. Test a point not on the line, e.g. (0,0):
0 > (1/2)(0) − 2 → 0 > −2 is true, so shade the region above the dashed line.

Result: dashed line through (0, −2) and (2, −1), with the half-plane above the line shaded.