Enter two sets of coordinates (x₁, y₁) and (x₂, y₂) to find the slope and equation.
Solve for y (Slope-Intercept Form)
Calculate the value of y using the formula: y = mx + b
Understanding Linear Equations
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. When graphed on a Cartesian plane, a linear equation always results in a straight line.
The Slope-Intercept Form
The most common way to represent a linear equation is the Slope-Intercept Form:
y = mx + b
m: The slope (gradient) of the line, which represents the rate of change.
b: The y-intercept, which is the point where the line crosses the y-axis.
x: The independent variable.
y: The dependent variable.
Finding the Slope from Two Points
If you have two points, (x₁, y₁) and (x₂, y₂), you can calculate the slope (m) using the formula:
m = (y₂ – y₁) / (x₂ – x₁)
Note: If x₁ equals x₂, the slope is undefined, indicating a vertical line.
Real-World Example
Imagine you are tracking a delivery truck. The truck starts 10 miles away from a depot (b = 10) and travels at a constant speed of 50 miles per hour (m = 50). To find its distance (y) after 3 hours (x):
y = 50(3) + 10 y = 150 + 10 = 160 miles
function calculateTwoPoints() {
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 resDiv = document.getElementById('resultTwoPoints');
if (isNaN(x1) || isNaN(y1) || isNaN(x2) || isNaN(y2)) {
resDiv.style.display = 'block';
resDiv.innerHTML = 'Please enter all four coordinate values.';
return;
}
if (x1 === x2) {
resDiv.style.display = 'block';
resDiv.innerHTML = 'Result: Vertical LineEquation: x = ' + x1 + 'Slope is undefined (division by zero).';
return;
}
var slope = (y2 – y1) / (x2 – x1);
var intercept = y1 – (slope * x1);
// Round to 4 decimal places for cleanliness
slope = Number(Math.round(slope + 'e4') + 'e-4');
intercept = Number(Math.round(intercept + 'e4') + 'e-4');
var equation = "y = " + slope + "x " + (intercept >= 0 ? "+ " + intercept : "- " + Math.abs(intercept));
resDiv.style.display = 'block';
resDiv.innerHTML = '
';
}
function calculateYValue() {
var m = parseFloat(document.getElementById('slope_m').value);
var b = parseFloat(document.getElementById('intercept_b').value);
var x = parseFloat(document.getElementById('input_x').value);
var resDiv = document.getElementById('resultSlopeIntercept');
if (isNaN(m) || isNaN(b) || isNaN(x)) {
resDiv.style.display = 'block';
resDiv.innerHTML = 'Please enter m, b, and x values.';
return;
}
var y = (m * x) + b;
y = Number(Math.round(y + 'e4') + 'e-4');
resDiv.style.display = 'block';
resDiv.innerHTML = '
' +
'Calculation: y = (' + m + ' × ' + x + ') + ' + b + " +
'Result: y = ' + y + '' +
'