How to find points by linear interpolation

I suggest make a function that solves for y = mx + b.

x = c(5,6)
y = c(0.45, 0.50)
m <- (y[2] - y[1]) / (x[2] - x[1]) # slope formula
b <- y[1]-(m*x[1]) # solve for b
m*(5.019802) + b

# same answer as the approx function
[1] 0.4509901

You just need to specify an xout value.

approx(x,y,xout=5.019802)
$x
[1] 5.019802

$y
[1] 0.4509901