Problem 52 - Introductory Algebra for College Students

Question

Describe how to calculate the slope of a line passing through two points.

Step-by-Step Solution

Answer

The slope of a line passing through two points can be calculated using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1, y_1) \) and \( (x_2, y_2) \) are points on the line.

Step 1: Identify the Points

Firstly, identify two points on the line, let's denote them as \( (x_1, y_1) \) and \( (x_2, y_2) \).

Step 2: Understand the Slope Formula

Understand that the formula to calculate the slope \( m \) between these two points is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Step 3: Apply the Slope Formula

Finally, substitute the coordinates of \( (x_1, y_1) \) and \( (x_2, y_2) \) into the formula and calculate the slope.