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Chapter 2: Problem 82

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

Short Answer

Expert verified
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 by step solution

01

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.
02

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.
03

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.
04

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.

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