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Fart 1 of 2 Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. \( (5,-9) \) and \( (8,-3) \) Select the correct choice below and fill in the answer box within your choice. A. The slope is B. The slope is undefined.

Ask by Savage Park. in the United States
Jan 25,2025

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The slope is 2 and the line rises.

Solución

**A. The slope is 2 and the line rises.** **Explanation:** To find the slope \( m \) of the line passing through the points \( (5, -9) \) and \( (8, -3) \), use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - (-9)}{8 - 5} = \frac{6}{3} = 2 \] Since the slope is positive (\( m = 2 \)), the line **rises** as you move from left to right.

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To find the slope of the line passing through the points \( (5, -9) \) and \( (8, -3) \), we use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here, \( (x_1, y_1) = (5, -9) \) and \( (x_2, y_2) = (8, -3) \). Plugging in the values, we get: \[ m = \frac{-3 - (-9)}{8 - 5} = \frac{-3 + 9}{3} = \frac{6}{3} = 2 \] The slope is 2, indicating that the line rises. So, the correct choice is: A. The slope is 2. --- If you're ever unsure about how to determine the slope, just remember that a positive slope means the line goes up as you move to the right, while a negative slope means it goes down. So, with a slope of 2, you're definitely climbing up that math mountain! Also, keep in mind that if two points have the same x-coordinate (like \( (2, 5) \) and \( (2, -1) \)), the slope becomes undefined because you’re trying to divide by zero - a big no-no in math! Just say "vertical line" and move on.

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