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Chapter 2: Problem 2

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 \((3,4)\)

Short Answer

Expert verified
The slope of the line passing through the points \((2,1)\) and \((3,4)\) is 3. The line rises.

Step by step solution

01

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.
02

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, \(m = \frac{4-1}{3-2} = 3\).
03

Determine the Line Direction

With the slope \(m=3\), which is a positive number, indicate the line rises.

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