Problem 7 - 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. $$(-2,4) \text { and }(-1,-1)$$

Step-by-Step Solution

Answer

The slope of the line passing through the points (-2,4) and (-1,-1) is -5, indicating a falling line.

Step 1: Substitute Points Into The Slope Formula

Let's denote the points as follows: \(A(-2,4)\) to be \(A(x_1,y_1)\) and \(B(-1,-1)\) to be \(B(x_2,y_2)\). Substitute the coordinates of these points into the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). After substitution, the formula becomes \(m = \frac{-1-4}{-1 - (-2)}\)

Step 2: Calculate the slope value

Calculating the difference in y-coordinates and x-coordinates gives us the equation \(m = \frac{-5}{1}\)

Step 3: Interpret the slope value

The slope is -5. The negative sign indicates that the line falls. If the slope were undefined the line would be vertical. If the slope value were 0, it would indicate a horizontal line.