Find the equation of a line containing the given pair of points (1,4) and (5,6)

This is a linear equation y = mx+b, where m is the slope and b, the y-intercept.
Since we know this graph passes through A(1,4) and B(5,6), we can find easily the equation:

1st- Calculate m = (y₂-y₁)/(x₂-x₁) → m = (6-4)/5-1) = 2/4 →m =1/2
Now y = (1/2) + b.

2nd. To calculate b, replace x and y by either the coordinate of A(1,4) or       B(5,6)
Let's take A where x = 1 and y = 4 for instance:
y =(1/2)x + b
4=(1/2)(1) + b
4=1/2 + b
4-1/2 = b  and b= 7/2

Finally te equation becomes: y = (1/2)x + 7/2