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.

Question

The inequality is:

\[
y \leq \frac{2}{5}x + 1
\]

Now, we'll evaluate each point:

1. **Point (10, 6)**:
\[
y = 6, \quad x = 10 \\
6 \leq \frac{2}{5}(10) + 1 \\
6 \leq 4 + 1 \\
6 \leq 5 \quad \text{(False)}
\]

2. **Point (-10, 6)**:
\[
y = 6, \quad x = -10 \\
6 \leq \frac{2}{5}(-10) + 1 \\
6 \leq -4 + 1 \\
6 \leq -3 \quad \text{(False)}
\]

3. **Point (10, 5.5)**:
\[
y = 5.5, \quad x = 10 \\
5.5 \leq \frac{2}{5}(10) + 1 \\
5.5 \leq 4 + 1 \\
5.5 \leq 5 \quad \text{(False)}
\]

4. **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.\
make this like a 6th grader wrote this

Answer 1

To see which of the points is a solution for the inequality \( y \leq \frac{2}{5}x + 1 \), we will plug in the \( x \) and \( y \) values for each point into the inequality.

The inequality is:

\[ y \leq \frac{2}{5}x + 1 \]

Now let's check each point:

1. Point (10, 6):

   • Here, \( y = 6 \) and \( x = 10 \).
   • We check: \[ 6 \leq \frac{2}{5}(10) + 1 \]
   • Calculate the right side: \[ \frac{2}{5}(10) = 4 \quad \text{so} \quad 4 + 1 = 5 \]
   • Now we have: \[ 6 \leq 5 \quad \text{(This is False)} \]

2. Point (-10, 6):

   • Here, \( y = 6 \) and \( x = -10 \).
   • We check: \[ 6 \leq \frac{2}{5}(-10) + 1 \]
   • Calculate the right side: \[ \frac{2}{5}(-10) = -4 \quad \text{so} \quad -4 + 1 = -3 \]
   • Now we have: \[ 6 \leq -3 \quad \text{(This is False)} \]

3. Point (10, 5.5):

   • Here, \( y = 5.5 \) and \( x = 10 \).
   • We check: \[ 5.5 \leq \frac{2}{5}(10) + 1 \]
   • Calculate the right side: \[ \frac{2}{5}(10) = 4 \quad \text{so} \quad 4 + 1 = 5 \]
   • Now we have: \[ 5.5 \leq 5 \quad \text{(This is False)} \]

4. Point (10, 4):

   • Here, \( y = 4 \) and \( x = 10 \).
   • We check: \[ 4 \leq \frac{2}{5}(10) + 1 \]
   • Calculate the right side: \[ \frac{2}{5}(10) = 4 \quad \text{so} \quad 4 + 1 = 5 \]
   • Now we have: \[ 4 \leq 5 \quad \text{(This is True)} \]

So after checking all the points, the only point that works with the inequality \( y \leq \frac{2}{5}x + 1 \) is (10, 4).

Therefore, (10, 4) is part of the solution set for the inequality!