Slope

Slope is a measure of how steep a line is. It is the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line.

The formula for finding the slope (m) between two points (x1, y1) and (x2, y2) on a line is:

m = (y2 - y1) / (x2 - x1)

This can also be visualized as:

m = ^{change in y}/_{change in x}

Types of Slope

There are three main types of slope:

1. Positive Slope: If a line goes up from left to right, it has a positive slope. A positive slope indicates that as x increases, y also increases.
2. Negative Slope: If a line goes down from left to right, it has a negative slope. A negative slope indicates that as x increases, y decreases.
3. Zero Slope: A line with a slope of zero is a horizontal line where y remains constant as x changes.

Using Slope in Equations

Slope can be used in the equation of a line (y = mx + b), where m is the slope and b is the y-intercept. The slope-intercept form of a line is helpful for graphing and making predictions.

Study Guide

To study slope effectively, follow these steps:

1. Understand the concept of rise and run in relation to the slope.
2. Practice finding the slope between two points using the slope formula.
3. Identify and understand the different types of slope (positive, negative, zero).
4. Learn how to use slope in the equation of a line (y = mx + b).
5. Practice graphing lines using the slope-intercept form.

With a solid understanding of slope, you'll be able to analyze and interpret the steepness of lines and use this concept in various mathematical applications.