Question

Which of the following is a solution to this inequality?

y > (3/5)x - 2

A) (5, 0)
B) (0, -2)
C) (1, 1)
D) (-5, -6)

Answer 1

C) (1, 1)

Step-by-step explanation:

y > (3/5)x - 2

say it out loud :

y must be greater than (3/5)x - 2

for A) y must be greater than (3/5)×5 - 2 = 3 - 2 = 1.

but y = 0.

0 is NOT greater than 1. so, this is NOT a solution.

for B) y must be greater than (3/5)×0 - 2 = 0 - 2 = -2.

but y = -2.

-2 is NOT greater than -2. so, this is NOT a solution.

for C) y must be greater than (3/5)×1 - 2 = 3/5 - 2 = 3/5 - 10/5 = -7/5

y = 1.

1 is greater than -7/5, so this IS a solution.

for D) y must be greater than (3/5)×-5 - 2 = -3 - 2 = -5.

but y = -6

-6 is NOT greater than -5. so, this is NOT a solution.

Answer 2

The question asks for a solution to the inequality y > (3/5)x - 2. Options C and D make the inequality true when substituted, thereby acting as solutions.

Step-by-step explanation:

The question is asking to find which point is a solution to the inequality y > (3/5)x - 2. To find the solution, each option is substituted into the inequality to check if it makes the inequality true.

• For option A (5, 0), the inequality would be 0 > (3/5)*5 - 2 which simplifies to 0 > 1, which is false.
• For option B (0, -2), the inequality would be -2 > (3/5)*0 - 2 which simplifies to -2 > -2, which is also false since -2 is not greater than -2.
• For option C (1, 1), the inequality would be 1 > (3/5)*1 - 2 which simplifies to 1 > -1.2 which is true.
• For option D (-5, -6), the inequality would be -6 > (3/5)*(-5) - 2 which simplifies to -6 > -5 - 2 or -6 > -7 which is true.

Therefore, the solutions to the inequality that make it true are options C and D.