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 (−10,6) left parenthesis negative 10 comma 6 right parenthesis (10,4) left parenthesis 10 comma 4 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 need to substitute the x-coordinate of each point into the equation \( y = \frac{2}{5}x + 1 \) to find the corresponding y-value and then check if the actual y-value of the point is less than or equal to this calculated value.

1. **Point (10, 6)**:
\[
y = \frac{2}{5}(10) + 1 = 4 + 1 = 5
\]
Here, \( 6 \leq 5 \) is **false**.

2. **Point (-10, 6)**:
\[
y = \frac{2}{5}(-10) + 1 = -4 + 1 = -3
\]
Here, \( 6 \leq -3 \) is **false**.

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

4. **Point (10, 5.5)**:
\[
y = \frac{2}{5}(10) + 1 = 4 + 1 = 5
\]
Here, \( 5.5 \leq 5 \) is **false**.

The only point that satisfies the inequality \( y \leq \frac{2}{5}x + 1 \) is:

**(10, 4)**.