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)
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)
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