show which of the following points is part of the solution set for the inequality y<=(2)/(5)x+1 A:(10,4) B: (10,6) C: (-10,6) D: (10,5.5)
To determine which of the given points is part of the solution set for the inequality y ≤ (2/5)x + 1, we will substitute the x and y values of each point into the inequality and check if the inequality holds true.
A: (10,4)
Substituting x = 10 and y = 4 into the inequality, we get:
4 ≤ (2/5)(10) + 1
4 ≤ 4 + 1
4 ≤ 5
The inequality holds true for point A.
B: (10,6)
Substituting x = 10 and y = 6 into the inequality, we get:
6 ≤ (2/5)(10) + 1
6 ≤ 4 + 1
6 ≤ 5
The inequality does not hold true for point B.
C: (-10,6)
Substituting x = -10 and y = 6 into the inequality, we get:
6 ≤ (2/5)(-10) + 1
6 ≤ -4 + 1
6 ≤ -3
The inequality does not hold true for point C.
D: (10,5.5)
Substituting x = 10 and y = 5.5 into the inequality, we get:
5.5 ≤ (2/5)(10) + 1
5.5 ≤ 4 + 1
5.5 ≤ 5
The inequality does not hold true for point D.
Therefore, the only point from the given options that is part of the solution set for the inequality is A: (10,4).