Problem 82 - College Algebra

Question

What is the slope of a line and how is it found?

Step-by-Step Solution

Answer

The slope of a line, represented by 'm', is a numerical measure of its steepness, found by the formula m = (y2 - y1) / (x2 - x1). You calculate it by choosing any two points on the line, subtracting their y-coordinates to get the rise and their x-coordinates to get the run, and then dividing the rise by the run.

Step 1: Define the slope of a line

The slope of a line, often represented by the letter 'm', is a measure that describes the direction and the steepness of the line. It can be positive, negative, zero, or undefined.

Step 2: Explain the concept of rise and run

In the context of a line on a graph, 'rise' refers to the change in the y-coordinate (vertical change), while 'run' refers to the change in the x-coordinate (horizontal change). These two measurements are used to calculate the slope.

Step 3: Explain the formula for calculating the slope

The slope of a line can be found by using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are coordinates of any two points on the line.

Step 4: Describe how to use the formula

To calculate the slope: first, choose any two points on the line and identify their coordinates. Then, subtract the y-coordinates (to find the rise) and the x-coordinates (to find the run). Finally, divide the rise by the run to find the slope.