Show which of the following points is part of the solution set for the inequality y <= 2/5x + 1.
(10,4)
(10,6)
(-10,6)
(10,5.5)
To determine which points are part of the solution set for the inequality y <= 2/5x + 1, substitute the x and y values from each point into the inequality and check if the inequality is true or false.
For the point (10,4):
4 <= (2/5)(10) + 1
4 <= 4 + 1
4 <= 5
This inequality is true, so (10,4) is part of the solution set.
For the point (10,6):
6 <= (2/5)(10) + 1
6 <= 4 + 1
6 <= 5
This inequality is false, so (10,6) is not part of the solution set.
For the point (-10,6):
6 <= (2/5)(-10) + 1
6 <= -4 + 1
6 <= -3
This inequality is false, so (-10,6) is not part of the solution set.
For the point (10,5.5):
5.5 <= (2/5)(10) + 1
5.5 <= 4 + 1
5.5 <= 5
This inequality is false, so (10,5.5) is not part of the solution set.
Therefore, the only point that is part of the solution set for the inequality y <= 2/5x + 1 is (10,4).