Questions: 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. (4,-2) and (6,-8) Select the correct choice below and fill in the answer box within your choice. A. The slope is ( Simplify your answer.) B. The slope is undefined.

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. (4,-2) and (6,-8) Select the correct choice below and fill in the answer box within your choice. A. The slope is ( Simplify your answer.) B. The slope is undefined.
Transcript text: 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. \[ (4,-2) \text { and }(6,-8) \] Select the correct choice below and fill in the answer box within your choice. A. The slope is $\square$ ( Simplify your answer.) B. The slope is undefined.
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Solution

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Solution Steps

Step 1: Identify the Points

The given points are \((x_1, y_1) = (4, -2)\) and \((x_2, y_2) = (6, -8)\).

Step 2: Apply the Slope Formula

The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).

Step 3: Calculate the Slope

Substituting the given points into the slope formula gives \(m = \frac{-8 + 2}{6 - 4}\). This simplifies to \(m = -3\).

Final Answer:

The slope of the line passing through the points \((4, -2)\) and \((6, -8)\) is -3.

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