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, 1
y<−
2
1
​
x−1
y, is less than, start fraction, 3, divided by, 5, end fraction, x, minus, 3
y<
5
3
​
x−3
x
y
Answer
Multiple Choice Answers
left parenthesis, 6, comma, minus, 3, right parenthesis(6,−3)
left parenthesis, minus, 10, comma, 8, right parenthesis(−10,8)
left parenthesis, minus, 7, comma, minus, 10, right parenthesis(−7,−10)
left parenthesis, minus, 3, comma, minus, 3, right parenthesis(−3,−3)

Answer 1

Test each point in both inequalities y < -(1/2)x - 1 and y < (3/5)x - 3.

(6, −3):
-(1/2)(6) − 1 = −4, and −3 < −4 is false → fails.

(−10, 8):
-(1/2)(−10) − 1 = 4, and 8 < 4 is false → fails.

(−7, −10):
-(1/2)(−7) − 1 = 2.5, and −10 < 2.5 is true;
(3/5)(−7) − 3 = −7.2, and −10 < −7.2 is true → satisfies both.

(−3, −3):
-(1/2)(−3) − 1 = 0.5, and −3 < 0.5 is true;
(3/5)(−3) − 3 = −4.8, and −3 < −4.8 is false → fails.

Answer: (−7, −10).