Show which of the following points is part of the solution set for the inequality y≤2/5x+1

Question

.(1 point)
Responses

(10,4)

left parenthesis 10 comma 4 right parenthesis
(10,5.5)
left parenthesis 10 comma 5.5 right parenthesis
(−10,6)
left parenthesis negative 10 comma 6 right parenthesis
(10,6)

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 need to check which points satisfy the inequality.

First, let's write the equation of the line for the boundary of the inequality:

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

Now we will evaluate each point in relation to this equation.

1. Point (10, 4): \[ y = \frac{2}{5}(10) + 1 = 4 + 1 = 5 \] Here, \( 4 \leq 5 \) is true. So, (10, 4) satisfies the inequality.

2. Point (10, 5.5): \[ y = \frac{2}{5}(10) + 1 = 4 + 1 = 5 \] Here, \( 5.5 \leq 5 \) is false. So, (10, 5.5) does not satisfy the inequality.

3. Point (-10, 6): \[ y = \frac{2}{5}(-10) + 1 = -4 + 1 = -3 \] Here, \( 6 \leq -3 \) is false. So, (-10, 6) does not satisfy the inequality.

4. Point (10, 6): \[ y = \frac{2}{5}(10) + 1 = 4 + 1 = 5 \] Here, \( 6 \leq 5 \) is false. So, (10, 6) does not satisfy the inequality.

Based on this evaluation, the only point that is part of the solution set is:

(10, 4).