Constant Rate of Change Graph Calculator
.crc-calculator-container {
max-width: 800px;
margin: 0 auto;
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
background: #f9f9f9;
padding: 30px;
border-radius: 12px;
box-shadow: 0 4px 15px rgba(0,0,0,0.1);
}
.crc-calculator-header {
text-align: center;
margin-bottom: 25px;
}
.crc-calculator-header h2 {
color: #2c3e50;
margin: 0;
font-size: 24px;
}
.crc-input-grid {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 20px;
margin-bottom: 25px;
}
.crc-input-group {
display: flex;
flex-direction: column;
}
.crc-input-group label {
font-weight: 600;
margin-bottom: 8px;
color: #34495e;
font-size: 14px;
}
.crc-input-group input {
padding: 12px;
border: 1px solid #ddd;
border-radius: 6px;
font-size: 16px;
transition: border-color 0.3s;
}
.crc-input-group input:focus {
border-color: #3498db;
outline: none;
}
.crc-btn {
width: 100%;
padding: 14px;
background-color: #3498db;
color: white;
border: none;
border-radius: 6px;
font-size: 16px;
font-weight: bold;
cursor: pointer;
transition: background-color 0.3s;
margin-bottom: 20px;
}
.crc-btn:hover {
background-color: #2980b9;
}
.crc-results-area {
background: white;
padding: 20px;
border-radius: 8px;
border: 1px solid #e0e0e0;
margin-top: 20px;
}
.crc-equation-display {
text-align: center;
font-size: 20px;
font-weight: bold;
color: #2c3e50;
margin-bottom: 20px;
padding: 10px;
background: #f0f8ff;
border-radius: 4px;
}
.crc-canvas-container {
width: 100%;
overflow-x: auto;
display: flex;
justify-content: center;
margin-bottom: 20px;
}
canvas {
border: 1px solid #ccc;
background-color: #fff;
}
.crc-table-container {
margin-top: 20px;
overflow-x: auto;
}
.crc-data-table {
width: 100%;
border-collapse: collapse;
font-size: 14px;
}
.crc-data-table th, .crc-data-table td {
border: 1px solid #ddd;
padding: 8px;
text-align: center;
}
.crc-data-table th {
background-color: #f2f2f2;
color: #333;
}
.crc-data-table tr:nth-child(even) {
background-color: #f9f9f9;
}
/* Content Styles */
.crc-content-section {
max-width: 800px;
margin: 40px auto;
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: #333;
}
.crc-content-section h2 {
color: #2c3e50;
margin-top: 30px;
}
.crc-content-section h3 {
color: #34495e;
margin-top: 20px;
}
.crc-content-section p {
margin-bottom: 15px;
}
.crc-content-section ul {
margin-bottom: 15px;
padding-left: 20px;
}
.crc-content-section li {
margin-bottom: 8px;
}
@media (max-width: 600px) {
.crc-input-grid {
grid-template-columns: 1fr;
}
}
function calculateCRCGraph() {
// 1. Get Input Values
var b = parseFloat(document.getElementById('initialValue').value);
var m = parseFloat(document.getElementById('rateOfChange').value);
var xMax = parseFloat(document.getElementById('xLimit').value);
var xLabel = document.getElementById('xLabelInput').value || "x";
// Validation
if (isNaN(b) || isNaN(m) || isNaN(xMax)) {
alert("Please enter valid numeric values for Initial Value, Rate of Change, and Limit.");
return;
}
if (xMax = 0) ? "+" : "-";
var bDisplay = Math.abs(b);
document.getElementById('equationDisplay').innerHTML =
"Equation: y = " + m + "x " + operator + " " + bDisplay;
document.getElementById('th-x').innerText = xLabel;
document.getElementById('th-y').innerText = "Output (y)";
// 3. Generate Table Data
var tableBody = document.getElementById('tableBody');
tableBody.innerHTML = ""; // Clear previous
var step = xMax / 10;
for (var i = 0; i <= 10; i++) {
var xVal = i * step;
var yVal = (m * xVal) + b;
// Fix decimals
xVal = Math.round(xVal * 100) / 100;
yVal = Math.round(yVal * 100) / 100;
var row = "
| " + xVal + " | " + yVal + " |
";
tableBody.innerHTML += row;
}
// 4. Draw Graph on Canvas
drawGraph(m, b, xMax, xLabel);
}
function drawGraph(m, b, xMax, xLabel) {
var canvas = document.getElementById('graphCanvas');
var ctx = canvas.getContext('2d');
var width = canvas.width;
var height = canvas.height;
var padding = 40;
// Clear canvas
ctx.clearRect(0, 0, width, height);
// Calculate Y range
// We calculate y at x=0 and x=xMax
var yStart = b;
var yEnd = (m * xMax) + b;
var minY = Math.min(yStart, yEnd, 0); // Include 0 in range
var maxY = Math.max(yStart, yEnd, 0);
// Add some padding to Y range so lines don't touch edges
var rangeY = maxY – minY;
if(rangeY === 0) rangeY = 10; // Handle horizontal line
minY = minY – (rangeY * 0.1);
maxY = maxY + (rangeY * 0.1);
// Mapping functions
function mapX(x) {
return padding + (x / xMax) * (width – 2 * padding);
}
function mapY(y) {
return height – padding – ((y – minY) / (maxY – minY)) * (height – 2 * padding);
}
// Draw Grid and Axes
ctx.beginPath();
ctx.strokeStyle = "#e0e0e0";
ctx.lineWidth = 1;
// Vertical Grid lines
for(var i=0; i<=10; i++) {
var xVal = (i/10) * xMax;
var px = mapX(xVal);
ctx.moveTo(px, padding);
ctx.lineTo(px, height – padding);
}
// Horizontal Grid lines
for(var j=0; j= padding && x0 = padding && y0 <= height – padding) {
ctx.moveTo(padding, y0);
ctx.lineTo(width – padding, y0);
} else {
// Draw bottom border if y=0 is out of view
ctx.moveTo(padding, height – padding);
ctx.lineTo(width – padding, height – padding);
}
ctx.stroke();
// Draw the Function Line
ctx.beginPath();
ctx.strokeStyle = "#e74c3c"; // Red color for the line
ctx.lineWidth = 3;
var startX = 0;
var startY = (m * startX) + b;
var endX = xMax;
var endY = (m * endX) + b;
ctx.moveTo(mapX(startX), mapY(startY));
ctx.lineTo(mapX(endX), mapY(endY));
ctx.stroke();
// Labels
ctx.fillStyle = "#000";
ctx.font = "12px Arial";
ctx.textAlign = "center";
// X Label
ctx.fillText(xLabel, width / 2, height – 10);
// Y Label
ctx.save();
ctx.translate(15, height / 2);
ctx.rotate(-Math.PI / 2);
ctx.fillText("Output (y)", 0, 0);
ctx.restore();
// Value Labels on Axes
ctx.fillText("0", mapX(0), mapY(0) + 15);
ctx.fillText(Math.round(xMax), mapX(xMax), mapY(0) + 15);
// Max Y label logic
ctx.fillText(Math.round(maxY), x0 – 15, padding + 5);
ctx.fillText(Math.round(minY), x0 – 15, height – padding);
}
Constant Rate of Change Graph Calculator
Welcome to the Constant Rate of Change Graph Calculator. This tool helps you visualize and calculate values for linear relationships found in mathematics, physics, and economics. Whether you are a student solving algebra problems or a professional analyzing trends, this calculator provides an instant visual representation of linear functions.
What is Constant Rate of Change?
A constant rate of change describes a relationship between two variables where one variable changes by a fixed amount for every unit increase in the other variable. In algebra, this is known as a linear function.
The graph of a constant rate of change is always a straight line. This relationship is mathematically expressed using the slope-intercept form equation:
y = mx + b
- y: The output (dependent variable).
- x: The input (independent variable).
- m (Rate of Change/Slope): How much y changes for every 1 unit of x.
- b (Initial Value/Y-Intercept): The value of y when x is zero.
How to Use This Calculator
Using this calculator is straightforward. You only need to identify the two key components of your linear relationship:
- Enter the Initial Value (b): This is your starting point. For example, if you have a flat fee of $5 before paying an hourly rate, enter 5. On a graph, this is where the line crosses the vertical Y-axis.
- Enter the Rate of Change (m): This represents the speed or rate of the trend. For example, if you travel at 60 miles per hour, enter 60. If you are losing 2 units per day, enter -2.
- Set the Limit: Define how far along the horizontal X-axis you want to calculate (e.g., 10 hours, 50 miles).
- Click Generate: The calculator will produce the specific linear equation, a data table of values, and a visual graph of the line.
Real-World Examples
1. Physics: Constant Velocity
If a car drives at a constant speed of 45 mph and starts 10 miles past the starting line:
- Initial Value (b): 10 (miles)
- Rate of Change (m): 45 (miles per hour)
- Equation: y = 45x + 10
2. Economics: Cost Functions
A service charges a $100 booking fee plus $50 per hour:
- Initial Value (b): 100 (Booking Fee)
- Rate of Change (m): 50 (Hourly Rate)
- Equation: y = 50x + 100
3. Filling a Tank
A water tank has 500 gallons and is draining at a rate of 20 gallons per minute:
- Initial Value (b): 500
- Rate of Change (m): -20 (Negative because it is draining)
- Equation: y = -20x + 500
Understanding the Graph
Steepness: A higher "Rate of Change" (m) results in a steeper line. A rate of 0 results in a perfectly horizontal line.
Direction: A positive rate (m > 0) means the line goes up from left to right (growth). A negative rate (m < 0) means the line goes down from left to right (decay).