Show which of the following points is part of the solution set for the inequality y≤25x+1 .(1 point)
(-10.6)
(10,4)
(10,5.5)
(10,6)
To determine which point is part of the solution set for the inequality y ≤ 25x + 1, we need to substitute the x and y values of each point into the inequality and check if the inequality holds true.
For (-10.6):
Substituting x = -10.6 and y = -10.6 into the inequality:
-10.6 ≤ 25(-10.6) + 1
-10.6 ≤ -265 + 1
-10.6 ≤ -264
Since -10.6 is not less than or equal to -264, (-10.6) is not part of the solution set.
For (10,4):
Substituting x = 10 and y = 4 into the inequality:
4 ≤ 25(10) + 1
4 ≤ 250 + 1
4 ≤ 251
Since 4 is less than or equal to 251, (10, 4) is part of the solution set.
For (10,5.5):
Substituting x = 10 and y = 5.5 into the inequality:
5.5 ≤ 25(10) + 1
5.5 ≤ 250 + 1
5.5 ≤ 251
Since 5.5 is less than or equal to 251, (10, 5.5) is part of the solution set.
For (10,6):
Substituting x = 10 and y = 6 into the inequality:
6 ≤ 25(10) + 1
6 ≤ 250 + 1
6 ≤ 251
Since 6 is less than or equal to 251, (10, 6) is part of the solution set.
Therefore, the points (10, 4), (10, 5.5), and (10, 6) are all part of the solution set for the inequality y ≤ 25x + 1.