Problem 73 - College Algebra Essentials

Question

Find the slope of the line passing through each pair of points or state that the slope is undefined. Assume that all variables represent positive real numbers. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $$(0, a) \text { and }(b, 0)$$

Step-by-Step Solution

Answer

The slope of the line passing through points (0, a) and (b, 0) is -a / b, and the line is falling.

Step 1: Find the slope

First, calculate the slope of the line. You can do this using the formula \( m = (y_2 - y_1) / (x_2 - x_1) \). Plug in the coordinates to get \( m = (0 - a) / (b - 0) = -a / b \)

Step 2: Check if the slope is defined

Because both a and b represent positive real numbers, -a / b is a defined real number.

Step 3: Determine the direction of the line

Our slope, -a / b, is negative, which suggests that the line falls. Lines that have a negative slope decrease from left to right.