Question

By imagining where the shading should be, identify which point would satisfy BOTH inequalities.
y, is less than, minus, 3, x, minus, 2
y<−3x−2
y, is less than, start fraction, 3, divided by, 4, end fraction, x, plus, 5
y<
4
3
​
x+5

Answer 1

To satisfy BOTH inequalities you must have y less than each right-hand side at the same x. Test a point by plugging its coordinates into both inequalities; if both are true the point is in the shaded intersection.

Example tests:
- (0, −3): plug into y < −3x − 2 → −3 < −2 (true). Plug into y < (3/4)x + 5 → −3 < 5 (true). So (0, −3) satisfies both.
- (−2, 0): 0 < −3(−2) − 2 = 4 (true) and 0 < (3/4)(−2) + 5 = 3.5 (true). So (−2, 0) also works.

If you have multiple-choice points, give them and I’ll test each.