show wich of the following points is part of the solution set for the inequality y<=(2)/(5)x+1 A: (0,-2/9) B: (0,-1/9) C: 0,-4/9) D: (0,-1/3)
To determine which point is part of the solution set for the inequality, we need to substitute the x and y coordinates of each point into the inequality and check if the inequality holds true.
Let's substitute the coordinates of each point into the inequality:
A: (0, -2/9)
Substituting the x-coordinate (0) and y-coordinate (-2/9) into the inequality:
-2/9 ≤ (2/5)(0) + 1
-2/9 ≤ 1
The inequality is true, so point A (0, -2/9) is part of the solution set.
B: (0, -1/9)
Substituting the x-coordinate (0) and y-coordinate (-1/9) into the inequality:
-1/9 ≤ (2/5)(0) + 1
-1/9 ≤ 1
The inequality is true, so point B (0, -1/9) is part of the solution set.
C: (0, -4/9)
Substituting the x-coordinate (0) and y-coordinate (-4/9) into the inequality:
-4/9 ≤ (2/5)(0) + 1
-4/9 ≤ 1
The inequality is true, so point C (0, -4/9) is part of the solution set.
D: (0, -1/3)
Substituting the x-coordinate (0) and y-coordinate (-1/3) into the inequality:
-1/3 ≤ (2/5)(0) + 1
-1/3 ≤ 1
The inequality is true, so point D (0, -1/3) is part of the solution set.
Therefore, all of the given points (A: (0, -2/9), B: (0, -1/9), C: (0, -4/9), and D: (0, -1/3)) are part of the solution set for the inequality.