Enter coordinates and click "Calculate Slope" to see the result.
function calculateSlope() {
var x1 = parseFloat(document.getElementById("x1_coord").value);
var y1 = parseFloat(document.getElementById("y1_coord").value);
var x2 = parseFloat(document.getElementById("x2_coord").value);
var y2 = parseFloat(document.getElementById("y2_coord").value);
var resultDiv = document.getElementById("slopeResult");
if (isNaN(x1) || isNaN(y1) || isNaN(x2) || isNaN(y2)) {
resultDiv.innerHTML = "Please enter valid numbers for all coordinates.";
resultDiv.className = "result error";
return;
}
var deltaX = x2 – x1;
var deltaY = y2 – y1;
if (deltaX === 0) {
if (deltaY === 0) {
resultDiv.innerHTML = "The two points are identical. Slope is undefined.";
resultDiv.className = "result error";
} else {
resultDiv.innerHTML = "The slope is undefined (vertical line).";
resultDiv.className = "result error";
}
} else {
var slope = deltaY / deltaX;
resultDiv.innerHTML = "The slope (m) is: " + slope.toFixed(4) + "";
resultDiv.className = "result";
}
}
Understanding Slope
The slope of a line is a measure of its steepness and direction. It describes how much the line rises or falls vertically for every unit it moves horizontally. In mathematics, the slope is often denoted by the letter 'm'.
The Slope Formula
To calculate the slope (m) between two points (x₁, y₁) and (x₂, y₂), we use the following formula:
m = (y₂ - y₁) / (x₂ - x₁)
This formula represents the "rise over run," where (y₂ – y₁) is the change in the y-coordinates (rise) and (x₂ – x₁) is the change in the x-coordinates (run).
Types of Slopes
Positive Slope: The line goes upwards from left to right. This means as x increases, y also increases. (e.g., m = 3)
Negative Slope: The line goes downwards from left to right. This means as x increases, y decreases. (e.g., m = -2)
Zero Slope: The line is perfectly horizontal. This occurs when y₂ – y₁ = 0, meaning there is no change in the y-coordinate. (e.g., m = 0)
Undefined Slope: The line is perfectly vertical. This occurs when x₂ – x₁ = 0, meaning there is no change in the x-coordinate, leading to division by zero. (e.g., x₁=x₂)
Practical Examples
Let's look at a few examples to illustrate how the slope calculator works:
Example 1: Positive Slope
Consider two points: Point 1 (1, 2) and Point 2 (3, 8).
x₁ = 1, y₁ = 2
x₂ = 3, y₂ = 8
Using the formula: m = (8 – 2) / (3 – 1) = 6 / 2 = 3. A positive slope of 3 indicates the line is rising steeply.
Example 2: Zero Slope (Horizontal Line)
Consider two points: Point 1 (0, 5) and Point 2 (4, 5).
x₁ = 0, y₁ = 5
x₂ = 4, y₂ = 5
Using the formula: m = (5 – 5) / (4 – 0) = 0 / 4 = 0. A slope of 0 means the line is perfectly horizontal.
Example 3: Undefined Slope (Vertical Line)
Consider two points: Point 1 (2, 1) and Point 2 (2, 7).
x₁ = 2, y₁ = 1
x₂ = 2, y₂ = 7
Using the formula: m = (7 – 1) / (2 – 2) = 6 / 0. Since division by zero is undefined, the slope is undefined, indicating a perfectly vertical line.
This calculator helps you quickly determine the slope between any two given points, providing a fundamental understanding of linear relationships in geometry and algebra.