Problem 10 - 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. $$(3,-4) \text { and }(3,5)$$

Step-by-Step Solution

Answer

The slope of the line passing through the points (3, -4) and (3, 5) is undefined, and the line is vertical.

Step 1: Identify the Coordinates

The coordinates given are point A(3, -4) and point B(3, 5). Therefore, for point A, x1 = 3 and y1 = -4. Similarly, for point B, x2 = 3 and y2 = 5.

Step 2: Apply the Slope Formula

Substitute the coordinates into the slope formula, which is \(\frac{y2 - y1}{x2 - x1}\). This gives us \(\frac{5 - (-4)}{3- 3}\). The denominator evaluates to 0, so the slope is undefined.

Step 3: Determining the Line's Orientation

Lines with an undefined slope are vertical lines. Therefore, the line that passes through points A and B is a vertical line.