How it works
The three points are assumed to lie on one nonvertical line. A known x outside the endpoints gives an extrapolation of that same line. This form solves for first point y-coordinate; enter the known quantities in First point x-coordinate, Second point x-coordinate, Second point y-coordinate, Known point x-coordinate, Known point y-coordinate.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| First point x-coordinate | 0 | Formula symbol: x1. Enter a numeric value. |
| Second point x-coordinate | 2 | Formula symbol: x2. Enter a numeric value. |
| Second point y-coordinate | 5 | Formula symbol: y2. Enter a numeric value. |
| Known point x-coordinate | 1 | Formula symbol: x. Enter a numeric value. |
| Known point y-coordinate | 3 | Formula symbol: y. Enter a numeric value. |
Worked example
Show example inputs and results
This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.
- First point x-coordinate
- 0
- Second point x-coordinate
- 2
- Second point y-coordinate
- 5
- Known point x-coordinate
- 1
- Known point y-coordinate
- 3
Complete example results
- First point y-coordinate
- 1
Reading the result
The result solves for first point y-coordinate from the entered quantities. Check the result unit and the formula conditions before using it.
Questions and answers
Can I use the example values for my own calculation?
The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.
When can I use the first point y-coordinate result?
A vertical line with x₂=x₁ has no unique y in this form. To solve an endpoint y, the known point cannot share that endpoint’s x-coordinate.
Why are some results rounded?
Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.
Are my inputs sent to a server?
The calculator processes inputs in your browser. Its code does not send your values to a server.
Method sources: openstax.org