Question

Below are two inequalities and the graphs of their lines without the shading. By imagining where the shading should be, identify which point would satisfy BOTH inequalities.
y, is less than, minus, one half, x, minus, 3
y<−
2
1
​
x−3
y, is less than, x, minus, 5
y<x−5
x
y
Answer
Multiple Choice Answers
left parenthesis, minus, 8, comma, minus, 6, right parenthesis(−8,−6)
left parenthesis, minus, 1, comma, minus, 8, right parenthesis(−1,−8)
left parenthesis, 7, comma, 1, right parenthesis(7,1)
left parenthesis, minus, 3, comma, 3, right parenthesis(−3,3)

Answer 1

Plug each point into both inequalities.

For (-1, -8):
- y < −(1/2)x − 3 → −8 < −(1/2)(−1) − 3 = 0.5 − 3 = −2.5 ⇒ true
- y < x − 5 → −8 < −1 − 5 = −6 ⇒ true

All other choices fail one or both inequalities. So the point is (−1, −8).