Problem 8 - 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. $$(6,-4) \text { and }(4,-2)$$

Step-by-Step Solution

Answer

The slope of the line passing through the points (6, -4) and (4, -2) is -1, which indicates that the line falls when moving from left to right.

Step 1: Identify the points

First, identify the two points given. In this case, the two points are (6, -4) and (4, -2). We name them as (x1, y1) and (x2, y2) respectively, so (x1, y1) = (6, -4) and (x2, y2) = (4, -2).

Step 2: Apply the formula for the slope

Use the formula for the slope of a line given two points, which is \((y2 - y1) / (x2 - x1)\). Substituting the values of (x1, y1) and (x2, y2), the formula becomes: \((-2 -(-4)) /(4 - 6)\). After simplification, the equation then becomes \((2 / -2)\).

Step 3: Simplify the slope and describe the direction

Simplify the equation to get the slope of the line. In this case, the slope is -1. Since the slope is negative, it means the line falls when moving from left to right. If the slope was positive, the line would rise; if it was 0, the line would be horizontal; and if the slope was undefined (the denominator (x2 - x1) equals to 0), the line would be vertical.