Problem 2
Question
Find the slope of the line passing through each 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. \((2,1)\) and \((3,4)\)
Step-by-Step Solution
Verified Answer
The slope of the line passing through the points \((2,1)\) and \((3,4)\) is 3. The line rises.
1Step 1: Identify the coordinates
Identify the coordinates for \((x_1, y_1)\) and \((x_2, y_2)\). Here, \((x_1, y_1) = (2,1)\) and \((x_2, y_2) = (3,4)\) respectively.
2Step 2: Substitute and Calculate the Slope
Using the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\), substitute in the values for \(x_1, y_1, x_2, y_2\) to calculate the slope. In this case, \(m = \frac{4-1}{3-2} = 3\).
3Step 3: Determine the Line Direction
With the slope \(m=3\), which is a positive number, indicate the line rises.
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