Question

Question
Show which of the following points is part of the solution set for the inequality y≤2/
5x+1
.(1 point)
Responses

(10,6)
left parenthesis 10 comma 6 right parenthesis

(10,4)
left parenthesis 10 comma 4 right parenthesis

(−10,6)
left parenthesis negative 10 comma 6 right parenthesis

(10,5.5)

Answer 1

To determine which of the given points is part of the solution set for the inequality \( y \leq \frac{2}{5}x + 1 \), we will substitute each point into the inequality and check if it satisfies the condition.

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

2. **For the point \( (10, 4) \)**:
\[
y = 4 \quad \text{and} \quad x = 10
\]
\[
\frac{2}{5}(10) + 1 = 4 + 1 = 5
\]
Check: \( 4 \leq 5 \) (True)

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

4. **For the point \( (10, 5.5) \)**:
\[
y = 5.5 \quad \text{and} \quad x = 10
\]
\[
\frac{2}{5}(10) + 1 = 4 + 1 = 5
\]
Check: \( 5.5 \leq 5 \) (False)

From our evaluations, the only point that satisfies the inequality \( y \leq \frac{2}{5}x + 1 \) is \( (10, 4) \).

Therefore, the point that is part of the solution set for the inequality is **(10, 4)**.