Welcome to our free online slope calculator! Whether you're a student tackling algebra homework or a professional working with linear relationships, our tool simplifies the process of finding and understanding slopes.
In mathematics, the slope (also known as gradient) is a measure of the steepness of a line. It represents the change in the y-coordinate (rise) divided by the change in the x-coordinate (run) between two points on a line. Understanding slope is crucial for graphing linear equations and analyzing relationships between variables.
Understanding and calculating slope has numerous real-world applications:
By mastering the concept of slope, you'll gain valuable insights into linear relationships across various fields. Our calculator makes it easy to visualize and understand these relationships, helping you excel in your studies or professional work.
Choose two points on your line. Let's call them (x₁, y₁) and (x₂, y₂).
Example: Let's use the points (2, 3) and (5, 9).
The slope formula is: m = (y₂ - y₁) / (x₂ - x₁)
Example: m = (9 - 3) / (5 - 2) = 6 / 3 = 2
Points: (0, 1) and (3, 7)
m = (7 - 1) / (3 - 0) = 6 / 3 = 2
The slope is 2, which means the line rises 2 units for every 1 unit it moves right.
Points: (1, 6) and (4, 0)
m = (0 - 6) / (4 - 1) = -6 / 3 = -2
The slope is -2, which means the line falls 2 units for every 1 unit it moves right.
Points: (2, 4) and (5, 4)
m = (4 - 4) / (5 - 2) = 0 / 3 = 0
The slope is 0, which means the line is horizontal.
Points: (3, 2) and (3, 7)
m = (7 - 2) / (3 - 3) = 5 / 0 = undefined
The slope is undefined, which means the line is vertical.
Remember, the order of the points doesn't matter as long as you're consistent. (x₁, y₁) can be either point, as long as (x₂, y₂) is the other point.