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, 4, x, plus, 3
y<−4x+3
y, is greater than, one sixth, x, plus, 4
y>
6
1
​
x+4
x
y
Answer
Multiple Choice Answers
left parenthesis, 3, comma, 3, right parenthesis(3,3)
left parenthesis, 9, comma, 6, right parenthesis(9,6)
left parenthesis, minus, 3, comma, minus, 2, right parenthesis(−3,−2)
left parenthesis, minus, 7, comma, 8, right parenthesis(−7,8)

Answer 1

Check each point in both inequalities y < −4x + 3 and y > (1/6)x + 4.

For (−7, 8):
- −4x + 3 = −4(−7) + 3 = 28 + 3 = 31, and 8 < 31 is true.
- (1/6)x + 4 = (−7)/6 + 4 ≈ 2.833, and 8 > 2.833 is true.

So (−7, 8) satisfies both inequalities.