Desmos Grphing Calculator

Desmos Linear Equation Generator

Use this calculator to find the linear equation (y = mx + b) that passes through two given points. You can then easily input this equation into Desmos to visualize the line.

Results:

Slope (m):

Y-intercept (b):

Linear Equation:

function calculateLinearEquation() { 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 slopeResult = document.getElementById('slope_result'); var yInterceptResult = document.getElementById('y_intercept_result'); var equationResult = document.getElementById('equation_result'); if (isNaN(x1) || isNaN(y1) || isNaN(x2) || isNaN(y2)) { slopeResult.textContent = "Invalid input"; yInterceptResult.textContent = "Invalid input"; equationResult.textContent = "Please enter valid numbers for all coordinates."; return; } if (x1 === x2) { // Vertical line slopeResult.textContent = "Undefined"; yInterceptResult.textContent = "N/A"; equationResult.textContent = "x = " + x1; } else { var m = (y2 – y1) / (x2 – x1); var b = y1 – m * x1; slopeResult.textContent = m.toFixed(4); yInterceptResult.textContent = b.toFixed(4); var equationString = "y = "; if (m === 0) { equationString += b.toFixed(4); } else { equationString += m.toFixed(4) + "x"; if (b !== 0) { equationString += (b > 0 ? " + " : " – ") + Math.abs(b).toFixed(4); } } equationResult.textContent = equationString; } } .calculator-container { background-color: #f9f9f9; border: 1px solid #ddd; padding: 20px; border-radius: 8px; max-width: 600px; margin: 20px auto; font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif; } .calculator-container h2 { color: #333; text-align: center; margin-bottom: 20px; } .calculator-container p { color: #555; line-height: 1.6; margin-bottom: 15px; } .calc-input-group { margin-bottom: 15px; } .calc-input-group label { display: block; margin-bottom: 5px; color: #333; font-weight: bold; } .calc-input-group input[type="number"] { width: calc(100% – 22px); padding: 10px; border: 1px solid #ccc; border-radius: 4px; box-sizing: border-box; } .calc-button { display: block; width: 100%; padding: 12px 20px; background-color: #007bff; color: white; border: none; border-radius: 4px; font-size: 16px; cursor: pointer; transition: background-color 0.3s ease; margin-top: 20px; } .calc-button:hover { background-color: #0056b3; } .calc-result-area { background-color: #e9ecef; border: 1px solid #dee2e6; padding: 15px; border-radius: 4px; margin-top: 25px; } .calc-result-area h3 { color: #333; margin-top: 0; margin-bottom: 10px; } .calc-result-area p { margin-bottom: 8px; color: #333; } .calc-result-area p strong { color: #000; }

Understanding Linear Equations with Desmos

Desmos is a powerful and intuitive online graphing calculator that makes visualizing mathematical functions incredibly easy. While Desmos itself is a tool for graphing, understanding the underlying equations is key to using it effectively. One of the most fundamental concepts in algebra and geometry is the linear equation, which represents a straight line on a graph.

What is a Linear Equation?

A linear equation is an algebraic equation in which each term has an exponent of 1, and when graphed, it always results in a straight line. The most common form of a linear equation is the slope-intercept form: y = mx + b.

  • y: The dependent variable (output value).
  • x: The independent variable (input value).
  • m: The slope of the line, which describes its steepness and direction. A positive slope means the line rises from left to right, while a negative slope means it falls.
  • b: The y-intercept, which is the point where the line crosses the y-axis (i.e., the value of y when x = 0).

How to Find a Linear Equation from Two Points

If you have two distinct points on a coordinate plane, you can always determine the unique linear equation that passes through them. This calculator simplifies that process for you. Here's the mathematical breakdown:

  1. Calculate the Slope (m): The slope is the "rise over run" between the two points. If your points are (x₁, y₁) and (x₂, y₂), the formula for the slope is:
    m = (y₂ - y₁) / (x₂ - x₁)
  2. Calculate the Y-intercept (b): Once you have the slope (m), you can use one of the points and the slope-intercept form (y = mx + b) to solve for 'b'. Substitute the values of x, y, and m into the equation:
    y₁ = m(x₁) + b
    Rearranging this gives you:
    b = y₁ - m(x₁)

Special Case: Vertical Lines If the x-coordinates of your two points are identical (x₁ = x₂), then the line is vertical. In this case, the slope is undefined, and the equation takes the form x = constant (where the constant is the shared x-coordinate).

Using This Calculator with Desmos

This Desmos Linear Equation Generator allows you to quickly find the slope, y-intercept, and the full equation of a line given any two points. Simply input the x and y coordinates for your two points into the fields above and click "Calculate Equation".

Once you have the equation, you can directly type it into the Desmos graphing calculator (e.g., y = 2x + 0 or y = -0.5x + 3) to instantly visualize the line. This is incredibly useful for checking your work, exploring relationships between points, or preparing data for more complex Desmos projects.

Experiment with different points to see how the slope and y-intercept change, and observe how these changes affect the line's appearance in Desmos.

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