Show which of the following points is part of the solution set for the inequality y <_ 2/5x +1.
A. (10, 5.5)
B. (10, 4)
C. (10, 6)
D. (-10, 6)
To determine which point is part of the solution set for the inequality, we substitute the x and y values of each point into the inequality and check if the inequality holds true.
For point A: (10, 5.5)
y ≤ (2/5)x + 1
5.5 ≤ (2/5)(10) + 1
5.5 ≤ 4 + 1
5.5 ≤ 5
This is not true, so point A is NOT part of the solution set.
For point B: (10, 4)
y ≤ (2/5)x + 1
4 ≤ (2/5)(10) + 1
4≤ 4 + 1
4 ≤ 5
This is true, so point B is part of the solution set.
For point C: (10, 6)
y ≤ (2/5)x + 1
6 ≤ (2/5)(10) + 1
6 ≤ 4 + 1
6 ≤ 5
This is not true, so point C is NOT part of the solution set.
For point D: (-10, 6)
y ≤ (2/5)x + 1
6 ≤ (2/5)(-10) + 1
6 ≤ -4 + 1
6 ≤ -3
This is not true, so point D is NOT part of the solution set.
Therefore, the point that is part of the solution set for the inequality is B. (10, 4)