You might know what slope is, but when you’re asked “What is the slope of a horizontal line?”, your mind goes blank. We’ll walk you through this answer, where it comes from, and how to calculate slope in other situations.
The Slope of a Horizontal and Vertical Line
The slope of a horizontal line is zero while the slope of a vertical line is undefined.
Slopes represent a line's ratio of vertical change to horizontal change. Because horizontal and vertical lines remain constant and never increase or decrease, they're merely straight lines.
Horizontal lines have no steepness at all. Because any calculation of the slope of horizontal lines means dividing zero by another number, the slope of a horizontal line is always zero.
A vertical line, on the other hand, is calculated by dividing a number by zero. Because you can’t divide by zero, vertical lines always have an undefined slope.
Finding the Slope of a Line
Now that we’ve learned that the slope of a horizontal line is zero, let's learn how to find the slopes of other linear equations.
Linear equations written as y=mx+b are in slope-intercept form. The m represents the slope and the b represents the y-intercept.
Slopes are often written in fraction form to represent how much movement there is between each given set of points. The numerator of the slope represents the increase in y-values and the denominator represents an increase in x-values. The slope of the equation below is :
The slope of the line determines how steep a line is and at what angle the line will hit its x-axis and y-axis. It will also determine whether the line will rise or fall. If you have a positive slope, like in equation 1, your values are increasing and the line will rise. If you have a negative slope, like in equation 2, they are decreasing and the line will fall.
Note that due to the integer 2 in equation 1, our line crosses the y-axis at (0, 2).
The Importance of Slopes
Slopes are an essential part of understanding and graphing a linear equation. When you see a horizontal, you can conclude the slope is zero. However, the slope of a vertical line is undefined.
When you see an angled line on a graph, you can use its change in horizontal and vertical values to determine the slope.