To determine which of the provided 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.
The inequality is:
\[ y \leq \frac{2}{5}x + 1 \]
Now, we'll evaluate each point:
-
Point (10, 6): \[ y = 6, \quad x = 10 \ 6 \leq \frac{2}{5}(10) + 1 \ 6 \leq 4 + 1 \ 6 \leq 5 \quad \text{(False)} \]
-
Point (-10, 6): \[ y = 6, \quad x = -10 \ 6 \leq \frac{2}{5}(-10) + 1 \ 6 \leq -4 + 1 \ 6 \leq -3 \quad \text{(False)} \]
-
Point (10, 5.5): \[ y = 5.5, \quad x = 10 \ 5.5 \leq \frac{2}{5}(10) + 1 \ 5.5 \leq 4 + 1 \ 5.5 \leq 5 \quad \text{(False)} \]
-
Point (10, 4): \[ y = 4, \quad x = 10 \ 4 \leq \frac{2}{5}(10) + 1 \ 4 \leq 4 + 1 \ 4 \leq 5 \quad \text{(True)} \]
From the evaluations, the only point that satisfies the inequality \( y \leq \frac{2}{5}x + 1 \) is (10, 4).
Therefore, (10, 4) is a part of the solution set for the inequality.