Calculate the average rate of change (slope) between two points.
Point 1 (Starting Coordinates)
Point 2 (Ending Coordinates)
Rate of Change (Slope)0
Vertical Change (Rise / Δy):0
Horizontal Change (Run / Δx):0
Calculation Formula:
Graph Behavior:—
function calculateGraphRate() {
// 1. Get Input Values
var x1 = document.getElementById('x1Val').value;
var y1 = document.getElementById('y1Val').value;
var x2 = document.getElementById('x2Val').value;
var y2 = document.getElementById('y2Val').value;
var xLabel = document.getElementById('xUnit').value.trim() || "unit";
var yLabel = document.getElementById('yUnit').value.trim() || "unit";
// 2. Validate Inputs
if (x1 === "" || y1 === "" || x2 === "" || y2 === "") {
alert("Please enter values for both Point 1 and Point 2.");
return;
}
var x1Num = parseFloat(x1);
var y1Num = parseFloat(y1);
var x2Num = parseFloat(x2);
var y2Num = parseFloat(y2);
if (isNaN(x1Num) || isNaN(y1Num) || isNaN(x2Num) || isNaN(y2Num)) {
alert("Please ensure all coordinates are valid numbers.");
return;
}
// 3. Calculate Differences (Delta)
var rise = y2Num – y1Num;
var run = x2Num – x1Num;
// 4. Handle Edge Case: Division by Zero (Vertical Line)
var rateText = "";
var behaviorText = "";
if (run === 0) {
rateText = "Undefined (Vertical Line)";
behaviorText = "Infinite Slope";
} else {
var rate = rise / run;
// Round to 4 decimal places for cleanliness, but keep precision if needed
rateText = parseFloat(rate.toFixed(4));
// Determine behavior
if (rate > 0) {
behaviorText = "Increasing (Positive Slope)";
} else if (rate < 0) {
behaviorText = "Decreasing (Negative Slope)";
} else {
behaviorText = "Constant (Horizontal Line)";
}
}
// 5. Update UI
document.getElementById('rate-result').style.display = 'block';
// Display main rate
document.getElementById('displayRate').innerHTML = rateText;
// Display units if available
if (run !== 0) {
document.getElementById('rateUnits').innerHTML = yLabel + " per " + xLabel;
} else {
document.getElementById('rateUnits').innerHTML = "";
}
// Display components
document.getElementById('displayRise').innerHTML = parseFloat(rise.toFixed(4)) + " (" + yLabel + ")";
document.getElementById('displayRun').innerHTML = parseFloat(run.toFixed(4)) + " (" + xLabel + ")";
// Display formula context
var formulaStr = "(" + y2Num + " – " + y1Num + ") / (" + x2Num + " – " + x1Num + ")";
document.getElementById('displayFormula').innerHTML = formulaStr;
document.getElementById('displayBehavior').innerHTML = behaviorText;
}
How to Calculate Rate of Change on a Graph
Calculating the rate of change on a graph allows you to understand how one quantity changes in relation to another. In physics, math, and economics, this is equivalent to finding the slope of the line connecting two points. Whether you are tracking the speed of a car (distance over time) or the growth of a business (revenue over years), the process remains the same.
1. Identify Your Coordinates
To calculate the rate, you first need to identify two distinct points on the line of the graph. These are typically written as coordinates $(x, y)$:
Point 1 $(x_1, y_1)$: Your starting point.
Point 2 $(x_2, y_2)$: Your ending point.
The X-axis usually represents the independent variable (like time), while the Y-axis represents the dependent variable (like distance or cost).
2. The Rate of Change Formula
The rate of change is the ratio of the vertical change to the horizontal change. This is famously known as "Rise over Run". The formula is:
Rate (m) = (y2 – y1) / (x2 – x1)
Where:
Rise $(y_2 – y_1)$: The change in the vertical value.
Run $(x_2 – x_1)$: The change in the horizontal value.
3. Interpreting the Result
Once you calculate the rate, the result tells you the direction and steepness of the line:
Positive Rate: The line goes up from left to right. The quantity is increasing.
Negative Rate: The line goes down from left to right. The quantity is decreasing.
Zero Rate: The line is horizontal. There is no change over time.
Real World Example: Calculating Velocity
Imagine a graph where the Y-axis is Distance (meters) and the X-axis is Time (seconds).
Point 1: At 2 seconds, the object is at 10 meters $(2, 10)$.
Point 2: At 5 seconds, the object is at 25 meters $(5, 25)$.