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Chapter 2: Problem 9

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. $$(5,3)\( and \)(5,-2)$$

Short Answer

Expert verified
The slope of the line passing through the points (5,3) and (5,-2) is undefined, indicating a vertical line.

Step by step solution

01

Identify the given points

The points given are (5,3) and (5,-2). For easier identification, let's call (5,3) as point 1 and represented by \(x1,y1\) and (5,-2) as point 2 and represented by \(x2, y2\).
02

Insert the values into the slope formula

We can apply the slope formula, \(m = \frac{y2 - y1}{x2 - x1}\). Replacing with our points we have: \(m = \frac{-2 - 3}{5 - 5}\)
03

Calculate the Slope

Solving the equation we get \(m = \frac{-5}{0}\). But any number divided by zero is undefined.
04

Identify the type of line

Since the slope is undefined, the line through the points is vertical.

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