Problem 6 - 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. $$(4,-1) \text { and }(3,-1)$$

Step-by-Step Solution

Answer

The slope of a line passing through the points (4,-1) and (3,-1) is 0, so the line is horizontal.

Step 1: Define the Points

First, define the coordinates of the allocated points: Point 1 is at (4,-1) and Point 2 is at (3,-1). This gives us \(x_1 = 4, y_1 = -1, x_2 = 3, y_2 = -1\)

Step 2: Apply the Slope Formula

Apply the formula for the slope of a line: \((y_2-y_1)/(x_2-x_1)\) Substitute the defined coordinates into the slope formula to get: \((-1- (-1))/(3 - 4) = 0\). Therefore, the slope of the line passing through points (4,-1) and (3,-1) is 0.

Step 3: Determine the Line Direction

By convention, a slope of 0 corresponds to a horizontal line. Therefore, our line is a horizontal line