Is y-4=3(x+1) an equation of a lone through (-2,1)? Explain.?

When x = -2 and y = 1 :

L.H.S. = (1) - 4 = -3
R.H.S. = 3((-2) + 1) = -3

Since L.H.S. = R.H.S.
then the equation y - 4 = 3(x + 1) passes through (-2, 1).