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

(10,5.5)
left parenthesis 10 comma 5.5 right parenthesis

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

(−10,6)

Answer 1

To determine which of the points is part of the solution set for the inequality \( y \leq \frac{2}{5}x + 1 \), we need to evaluate each point by substituting the x-coordinate into the equation and checking if the corresponding y-coordinate satisfies the inequality.

The inequality is given by:

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

Let's evaluate each point:

1. **For (10, 6):**
\[
y = 6, \quad x = 10
\]
Calculate the right-hand side:
\[
\frac{2}{5}(10) + 1 = 4 + 1 = 5
\]
Check the inequality:
\[
6 \leq 5 \text{ (False)}
\]

2. **For (10, 5.5):**
\[
y = 5.5, \quad x = 10
\]
Calculate the right-hand side:
\[
\frac{2}{5}(10) + 1 = 4 + 1 = 5
\]
Check the inequality:
\[
5.5 \leq 5 \text{ (False)}
\]

3. **For (10, 4):**
\[
y = 4, \quad x = 10
\]
Calculate the right-hand side:
\[
\frac{2}{5}(10) + 1 = 4 + 1 = 5
\]
Check the inequality:
\[
4 \leq 5 \text{ (True)}
\]

4. **For (−10, 6):**
\[
y = 6, \quad x = -10
\]
Calculate the right-hand side:
\[
\frac{2}{5}(-10) + 1 = -4 + 1 = -3
\]
Check the inequality:
\[
6 \leq -3 \text{ (False)}
\]

From the evaluations above, the point that is part of the solution set for the inequality \( y \leq \frac{2}{5}x + 1 \) is:

**(10, 4)**.