Question

Show which of the following points is part of the solution set for the inequality y is less than or equal to 2/5x + 1.

A: (-10 , 6)

B: ( 10, 4)

C: ( 10, 6)

D: ( 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 can substitute the \( x \) and \( y \) values of each point into the inequality and check if it holds true.

The inequality is:
\[ y \leq \frac{2}{5}x + 1 \]

Let's evaluate each point:

**A: (-10, 6)**
Substituting \( x = -10 \) and \( y = 6 \):
\[ 6 \leq \frac{2}{5}(-10) + 1 \]
\[ 6 \leq -4 + 1 \]
\[ 6 \leq -3 \] (False)

**B: (10, 4)**
Substituting \( x = 10 \) and \( y = 4 \):
\[ 4 \leq \frac{2}{5}(10) + 1 \]
\[ 4 \leq 4 + 1 \]
\[ 4 \leq 5 \] (True)

**C: (10, 6)**
Substituting \( x = 10 \) and \( y = 6 \):
\[ 6 \leq \frac{2}{5}(10) + 1 \]
\[ 6 \leq 4 + 1 \]
\[ 6 \leq 5 \] (False)

**D: (10, 5.5)**
Substituting \( x = 10 \) and \( y = 5.5 \):
\[ 5.5 \leq \frac{2}{5}(10) + 1 \]
\[ 5.5 \leq 4 + 1 \]
\[ 5.5 \leq 5 \] (False)

After checking all options, we find that the only point that satisfies the inequality is:

**B: (10, 4)**.