Question

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:

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!