# Lesson 15: The Slope of a Nonvertical Line

In this lesson, we will learn about the slope, or steepness, of a nonvertical line. Slope is an important concept in mathematics that is used to describe the relationship between two variables. It is also used to find equations of lines, measure angles, and more. Understanding the definition and how to calculate the slope of a nonvertical line is essential for any mathematics student.

## Definition of Slope

Slope is defined as the rate of change between two points on a line graph. It is measured in terms of the number of units that change in the y-axis (vertical axis) for every one unit that changes in the x-axis (horizontal axis). This rate of change can be calculated by dividing the change in the y-axis by the change in the x-axis. This calculation is written as “m = Δy/Δx” and is commonly referred to as the slope formula.

## Calculating the Slope of a Nonvertical Line

The slope of a nonvertical line can be calculated by finding two points on the line and plugging them into the slope formula. The first point must have a known x and y value, and the second point must have a known x and y value. Once these values are plugged into the formula, the slope can be calculated. For example, if the first point has an x value of 3 and a y value of 5, and the second point has an x value of 7 and a y value of 11, then the slope can be calculated by plugging these values into the formula as follows: m = (11-5)/(7-3) = 6/4 = 1.5. This means that the slope of the line is 1.5.

## Applications of Slope

Slope is an important concept in mathematics because it can be used to find equations of lines. When two points on a line are known, the slope can be used to find the equation of the line. This equation can then be used to calculate the y-coordinate of any given x-coordinate. Slope can also be used to measure angles between two lines. The two lines must have two points in common, and the slope of each line must be calculated. The angles between the lines can then be calculated using the slopes. Finally, slope can be used to calculate the steepness of a line. This can be done by calculating the absolute value of the slope.

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In conclusion, slope is an important concept in mathematics that is used to describe the relationship between two variables. It can be used to find equations of lines, measure angles, and calculate the steepness of a line. Understanding the definition and how to calculate the slope of a nonvertical line is essential for any mathematics student.