To determine which of the given points is part of the solution set for the inequality \( y \leq \frac{2}{5}x + 1 \), we can substitute the \( x \) and \( y \) values of each point into the inequality and check if it holds true.
The inequality is: \[ y \leq \frac{2}{5}x + 1 \]
Let's evaluate each point:
A: (-10, 6)
Substituting \( x = -10 \) and \( y = 6 \):
\[ 6 \leq \frac{2}{5}(-10) + 1 \]
\[ 6 \leq -4 + 1 \]
\[ 6 \leq -3 \] (False)
B: (10, 4)
Substituting \( x = 10 \) and \( y = 4 \):
\[ 4 \leq \frac{2}{5}(10) + 1 \]
\[ 4 \leq 4 + 1 \]
\[ 4 \leq 5 \] (True)
C: (10, 6)
Substituting \( x = 10 \) and \( y = 6 \):
\[ 6 \leq \frac{2}{5}(10) + 1 \]
\[ 6 \leq 4 + 1 \]
\[ 6 \leq 5 \] (False)
D: (10, 5.5)
Substituting \( x = 10 \) and \( y = 5.5 \):
\[ 5.5 \leq \frac{2}{5}(10) + 1 \]
\[ 5.5 \leq 4 + 1 \]
\[ 5.5 \leq 5 \] (False)
After checking all options, we find that the only point that satisfies the inequality is:
B: (10, 4).