Line Equation Calculator

How to Use the Line Equation Calculator

This Line Equation Calculator is designed to help you find the equation of a line given two points on the coordinate plane. Follow the step-by-step guide below to learn how to use it effectively.

Step 1: Input Coordinates for the First Point

• Locate the field labeled X₁ (First Point).
• Enter the x-coordinate of the first point into this field. Make sure to input a number as it is a required field.
• Next, find the field labeled Y₁ (First Point).
• Enter the y-coordinate of the first point here. This is also a required field, so ensure you enter a valid number.

Step 2: Input Coordinates for the Second Point

• Locate the field labeled X₂ (Second Point).
• Enter the x-coordinate of the second point into this field. Again, be sure to input a number as it is a required field.
• Proceed to the field labeled Y₂ (Second Point).
• Input the y-coordinate of the second point here. This field is also required, so ensure you input a number.

Step 3: Calculate the Results

Upon entering all the required coordinates, the calculator will compute several key characteristics of the line:

• Slope (m): This is calculated using the formula (y2 – y1) / (x2 – x1) and will be displayed up to four decimal places.
• Y-Intercept (b): This is determined with the formula y1 – ((y2 – y1) / (x2 – x1)) * x1 and will also be shown to four decimal places.
• Slope-Intercept Form: This provides the line equation in the form of y = mx + b, formatted with a prefix of “y = ” and a suffix of “x + b”.
• Point-Slope Form: This representation is calculated as y – y1 = m(x – x1) and is displayed with two decimal places.
• Distance Between Points: The distance between the two points is computed based on the formula sqrt(pow(x2 – x1, 2) + pow(y2 – y1, 2)) and displayed in a format with four decimal places and a suffix of ” units”.

Step 4: Interpret the Results

Once you have your results, you can use them to understand the characteristics of the line connecting the two points you provided:

• Slope (m): Indicates how steep the line is.
• Y-Intercept (b): Shows where the line crosses the y-axis.
• Slope-Intercept Form: Easily plug values into this form to solve for y given any x value.
• Point-Slope Form: Useful for understanding the line’s relationship from one of the given points.
• Distance: Gives a direct measure of how far apart the two points are on the plane.

And that’s how you use the Line Equation Calculator to find the equation of a line based on two points. Make sure all entered values are correct to get the most accurate calculations.