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Chapter 2: Problem 93

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

Short Answer

Expert verified
The slope of a line is a measure of its direction and steepness, which 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 two points on the line.

Step by step solution

01

Defining the Slope

Slope of a line is a measure of the direction and the steepness of the line. It is also commonly known as the 'gradient'.
02

Understand the line

In a two dimensional space (a plane), a line can be identified using two coordinates on the line, usually represented as \((x_1, y_1)\) and \((x_2, y_2)\).
03

Apply the formula

The slope (m) of a line passing through these two points can be found using the formula: \(m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\). This formula is derived from the concept of 'rise over run' which refers to the increase in Y-coordinates (vertical change or rise) over the increase in X-coordinates (horizontal change or run). Here, \(y_2 - y_1\) represents the 'rise' and \(x_2 - x_1\) represents the 'run'.

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