Problem 75 - 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. $$(a, b) \text { and }(a, b+c)$$

Step-by-Step Solution

Answer

The slope of the line passing through the points (a, b) and (a, b+c) is undefined and the line is vertical.

Step 1: Identify the Coordinates

We have two points: (a, b) and (a, b+c). Here, \(x_1=a\), \(y_1=b\) and \(x_2=a\), \(y_2=b+c\).

Step 2: Apply the Slope Formula

The formula for a slope of a line is \(m=\frac{y_2-y_1}{x_2-x_1}\). Substituting \(y_2\), \(y_1\), \(x_2\), and \(x_1\) into the formula gives us \(m=\frac{(b+c)-b}{a-a} = \frac{c}{0}\).

Step 3: Identify the Slope and Direction of the Line

Any number divided by zero is undefined, hence the slope of the line is undefined. A line with an undefined slope is a vertical line.