Question

Show which of the following points is part of the solution set for the inequality y <= 2/5 * x + 1
(10, 6)
(- 10, 6)
(10, 5.5)
(10, 4)

Answer 1

To determine which of the given points satisfies the inequality \(y \leq \frac{2}{5}x + 1\), we can substitute the \(x\) and \(y\) values of each point into the inequality and check whether it holds true.

The inequality is \(y \leq \frac{2}{5}x + 1\).

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

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

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

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

Therefore, the point that is part of the solution set for the inequality \(y \leq \frac{2}{5}x + 1\) is \((10, 4)\).