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.
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Find the boundary line: We start by rewriting the inequality: \[ 25x + 15y = 200 \] This can be converted to slope-intercept form (y = mx + b): \[ 15y = -25x + 200 \implies y = -\frac{25}{15}x + \frac{200}{15} \implies y = -\frac{5}{3}x + \frac{40}{3} \]
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Determine the region: The inequality \( 25x + 15y \geq 200 \) means we are interested in the region above (and including) the line \( y = -\frac{5}{3}x + \frac{40}{3} \).
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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 \( 25x + 15y \geq 200 \).
- For each point (x, y):
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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 \( 25x + 15y \geq 200 \).