How do you solve a Linear function in Solidity?

Question

Helo guys, I have a big project, but one function in particular to calculate a value (y) in a linear equation. Let me explain:

A linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function.

I have a table with coordinates with two points like: X(minX, maxX) and Y(minY, ymaxY) that to form this coordinate plane. I need find Y for a given X.

I'm doing this:

    function calculateCoordinateY(
        int256 x,
        int256 minX,
        int256 maxX,
        int256 minY,
        int256 maxY
    ) internal pure returns (int256 _y) {
        /**
         * https://medium.com/not-zero/linear-equation-50a847f58665
         * minY = (a * minX) + b
         * maxY = (a * maxX) + b
         * a = (minY - maxY) / (minX - maxX);
         * b = ((minY * maxX) - (minX * maxY)) / (maxX - minX);
         * y = (a * x) + b;
         */
        _y =
            (((minY - maxY) * x) / (minX - maxX)) +
            (((minY * maxX) - (minX * maxY)) / (maxX - minX));
    }

But doesn't work.. For values ​​of small intervals it works very well, but when the values ​​increase, not much, more than 10 already gives an error.

        // Point test # 1 = works fine
        (-10 * 10**18, 0.02 * 10**18)
        // Point test # 2 = works fine
        (-9.63 * 10**18, 0.0257454545454546 * 10**18)
        // Point test # 3 = works fine
        (0, 0.0621454545454546 * 10**18));
        // Point test # 4 = works fine
        (0.556 * 10**18, 0.0635454545454546 * 10**18)
        // Point test # 5 = no match math
        (14.44 * 10**18, 0.0985454545454545 * 10**18)
        // Point test # 6 = no match math
        (15.00 * 10**18, 0.1 * 10**18)

Does anyone know where I went wrong?

If my question is not clear, please tell me, I try to clarify better

Answer 1

Apparently the math I was trying to use doesn't work in solidity.

I checked the same math in excel for example, and everything was fine.

So I kept searching and found this: Two Point Form https://www.cuemath.com/geometry/two-point-form/

So now I have:

    /**
     * Calculate rewards within a specific range.
     */
    function calculateCoordinateY(
        int256 x,
        int256 minX,
        int256 maxX,
        int256 minY,
        int256 maxY
    ) internal pure returns (int256 _y) {
        /**
         * https://docs.google.com/document/d/1OWWFLzC-qi5yQWTbGCaTOckSxIvRNPev_BiiZfQYJ_Q/edit?usp=sharing
         * Analyzing the values, we see that all intervals belong to linear functions.
         * So we can do this:
         * Two Point Form
         * https://www.cuemath.com/geometry/two-point-form/
         */
        _y = (((maxY - minY) / (maxX - minX)) * (x - maxX)) + maxY;
    }

And it works perfectly. But it works because my values ​​generate a positive function, if your curve is negative, check the math, on that site I indicated there are both ways.