A linear graph represents a straight line on a coordinate plane. It is defined by a linear equation, typically in the form y = mx + b, where:
y is the dependent variable (plotted on the vertical axis).
x is the independent variable (plotted on the horizontal axis).
m is the slope of the line, indicating its steepness and direction.
b is the y-intercept, the point where the line crosses the y-axis (i.e., where x = 0).
Calculating Slope (m)
The slope of a line passing through two distinct points (x1, y1) and (x2, y2) is calculated as the ratio of the change in the y-coordinates to the change in the x-coordinates. The formula is:
m = (y2 - y1) / (x2 - x1)
If x2 - x1 = 0, the line is vertical, and the slope is undefined.
Calculating Y-intercept (b)
Once the slope (m) is known, the y-intercept (b) can be calculated by rearranging the linear equation y = mx + b to b = y - mx. You can use either of the two given points (x1, y1) or (x2, y2) to find b. Using (x1, y1):
b = y1 - m * x1
Use Cases for Linear Graphs
Linear graphs and their associated equations are fundamental in mathematics and science, appearing in numerous real-world applications:
Physics: Describing motion with constant velocity, force-displacement relationships (Hooke's Law), Ohm's Law (voltage vs. current).
Economics: Modeling supply and demand curves, cost functions, revenue projections.
Engineering: Analyzing system behavior, calibration curves, material properties.
Everyday Life: Calculating travel time at a constant speed, estimating costs based on a fixed rate plus a base fee.
This calculator helps you quickly determine the essential properties (slope and y-intercept) of a line given two points, making it easier to understand and work with linear relationships.
function calculateLinearGraph() {
var x1 = parseFloat(document.getElementById("x1").value);
var y1 = parseFloat(document.getElementById("y1").value);
var x2 = parseFloat(document.getElementById("x2").value);
var y2 = parseFloat(document.getElementById("y2").value);
var resultDiv = document.getElementById("result");
resultDiv.style.display = 'none'; // Hide previous results
resultDiv.classList.remove('error');
// Validate inputs
if (isNaN(x1) || isNaN(y1) || isNaN(x2) || isNaN(y2)) {
resultDiv.textContent = "Please enter valid numbers for all coordinates.";
resultDiv.classList.add('error');
resultDiv.style.display = 'block';
return;
}
var deltaX = x2 – x1;
var deltaY = y2 – y1;
var slope;
var yIntercept;
var equation = "";
// Calculate slope
if (deltaX === 0) {
slope = "undefined";
equation = "x = " + x1; // Vertical line equation
resultDiv.textContent = "Slope: " + slope + " | Equation: " + equation;
resultDiv.classList.add('error'); // Indicate issue with standard calculation
} else {
slope = deltaY / deltaX;
// Calculate y-intercept using y = mx + b => b = y – mx
yIntercept = y1 – slope * x1;
equation = "y = " + slope.toFixed(2) + "x + " + yIntercept.toFixed(2);
resultDiv.textContent = "Slope (m): " + slope.toFixed(2) + " | Y-intercept (b): " + yIntercept.toFixed(2) + " | Equation: " + equation;
resultDiv.classList.remove('error');
}
resultDiv.style.display = 'block';
}