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Equation of a Line Calculator

Use this calculator to find the slope, y-intercept, and the equation of a straight line given any two points (x1, y1) and (x2, y2) on the line.

Understanding the Equation of a Line

A graphing calculator is an invaluable tool for visualizing mathematical functions. While a full interactive graphing tool is complex, understanding the fundamental components of a line is crucial. This calculator focuses on one of the most basic yet important aspects: finding the equation of a straight line when you know two points that lie on it.

The Slope-Intercept Form: y = mx + b

The most common way to represent a straight line is through its slope-intercept form: y = mx + b. Let's break down what each part means:

  • y: The dependent variable, representing the vertical position on the graph.
  • x: The independent variable, representing the horizontal position on the graph.
  • m: The slope of the line. This value tells you how steep the line is and in which direction it's going. A positive slope means the line rises from left to right, a negative slope means it falls, and a zero slope means it's a horizontal line.
  • b: The y-intercept. This is the point where the line crosses the y-axis (i.e., where x = 0).

Calculating the Slope (m)

The slope is defined as the "rise over run" – the change in y divided by the change in x between any two points on the line. If you have two points (x1, y1) and (x2, y2), the formula for the slope is:

m = (y2 - y1) / (x2 - x1)

It's important to note that if x2 - x1 equals zero, the line is vertical, and its slope is undefined. This calculator will identify such cases.

Calculating the Y-intercept (b)

Once you have the slope (m), you can find the y-intercept (b) by plugging one of your known points (x1, y1) and the calculated slope into the slope-intercept form (y = mx + b) and solving for b:

y1 = m * x1 + b

Rearranging this gives:

b = y1 - m * x1

Example Calculation

Let's say we have two points: (1, 2) and (3, 6).

  1. Calculate the slope (m):
    m = (6 - 2) / (3 - 1) = 4 / 2 = 2
  2. Calculate the y-intercept (b) using point (1, 2):
    2 = 2 * 1 + b
    2 = 2 + b
    b = 0
  3. Formulate the equation:
    y = 2x + 0 or simply y = 2x

This calculator automates these steps, providing you with the slope, y-intercept, and the final equation of the line.

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Calculation Results:

"; outputHTML += "Point 1: (" + x1 + ", " + y1 + ")"; outputHTML += "Point 2: (" + x2 + ", " + y2 + ")"; outputHTML += "Slope (m): " + (typeof slope === 'number' ? slope.toFixed(4) : slope) + ""; outputHTML += "Y-intercept (b): " + (typeof yIntercept === 'number' ? yIntercept.toFixed(4) : yIntercept) + ""; outputHTML += "Equation of the Line: " + equation + ""; resultDiv.innerHTML = outputHTML; }

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