Question

This graph shows the inequality 25x + 15y ≥ 200, and represents Lina’s earnings for lawn mowing and dog walking where x represents the number of lawns mowed and y represents the number of dogs walked. Which of the labeled points is a viable solution in this context?

Answer 1

To determine which labeled points (let's say A, B, C, and D) is a viable solution to the inequality \( 25x + 15y \geq 200 \), we need to test each point by substituting its coordinates (x, y) into the inequality.

1. **Find the boundary line**: We start by rewriting the inequality:
\[
25x + 15y = 200
\]
This can be converted to slope-intercept form (y = mx + b):
\[
15y = -25x + 200 \implies y = -\frac{25}{15}x + \frac{200}{15} \implies y = -\frac{5}{3}x + \frac{40}{3}
\]

2. **Determine the region**: The inequality \( 25x + 15y \geq 200 \) means we are interested in the region above (and including) the line \( y = -\frac{5}{3}x + \frac{40}{3} \).

3. **Test each labeled point (A, B, C, D)** by substituting the x and y coordinates into the inequality:

- For each point (x, y):
- Calculate \( 25x + 15y \).
- Check if \( 25x + 15y \geq 200 \).

4. **Identify viable points**: A point will be a viable solution if, when substituted into the inequality, the left-hand side is greater than or equal to 200.

If you provide the coordinates of labeled points A, B, C, and D, I can help you evaluate which one is viable based on the inequality \( 25x + 15y \geq 200 \).