Составить уравнение прямой, проходящей через две заданные точки

main = putStrLn "Hello, World!"

checkLine ::  (Float,Float) -> (Float,Float) -> (Float,Float) -> Bool                     
checkLine (x1,y1) (x2,y2) (x,y) = abs ((x-x1)/(x2-x1) - (y-y1)/(y2-y1)) < 1.0E-6
 
Main> checkLine (1,1) (2,2) (5,5)
True
Main> checkLine (1,1) (2,2) (5,6)
False

linefun :: (Double, Double) -> (Double, Double) -> String
linefun (x1, y1) (x2, y2) = "y = " ++ show k ++ " * x + " ++ show b where
    k = dy / dx
    b = y1 - k * x1
    dx = x2 - x1
    dy = y2 - y1
 
main = putStrLn $ linefun (0, 1) (1, 3)
 
{- Output:
y = 2.0 * x + 1.0
-}

linefun :: (Double, Double) -> (Double, Double) -> Double -> Double
linefun (x1, y1) (x2, y2) =
    let dx = x2 - x1
        dy = y2 - y1
        k = dy / dx
        b = y1 - k * x1 in
    \x -> k*x + b
 
printf f x = putStrLn $ "f( " ++ show x ++ " ) = " ++ show (f x)
 
main = mapM_ (printf $ linefun (0, 1) (1, 3)) [0..4]
 
{- Output:
f( 0.0 ) = 1.0
f( 1.0 ) = 3.0
f( 2.0 ) = 5.0
f( 3.0 ) = 7.0
f( 4.0 ) = 9.0
-}

lineCoeff :: (Num a) => (a, a) -> (a, a) -> (a, a, a)
lineCoeff (x1, y1) (x2, y2) = (a, b, c)
    where a = y2 - y1
          b = x1 - x2
          c = - x1 * y2 + x1 * y1 + x2 * y1 - x1 * y1