Problem 9 - Introductory and Intermediate Algebra for College Students 4th

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. $$(5,3) \text { and }(5,-2)$$

Step-by-Step Solution

Answer

The slope of the line is undefined, and the line is vertical.

Step 1: Identify the given points

The given points are (5,3) and (5,-2). So, we have (x1, y1) as (5,3) and (x2, y2) as (5,-2).

Step 2: Substitute the points into the slope formula

The formula for the slope of a line between two points \((x1, y1)\) and \((x2, y2)\) is \((y2-y1) / (x2-x1)\). Substituting our points into this formula gives us \((-2 - 3) / (5 - 5)\).

Step 3: Simplify the expression

After simplifying, we have \(-5 / 0\). But division by zero is undefined.

Step 4: Determine the nature of the line

Because division by zero is undefined, the slope of the line is undefined. This means the line passing through the points is vertical.