how to I find an equation of a line given two points on that line (not using a graph) example:(1,5)(2,7)

Use the standard linear equation form

y = mx + b.
The slope is m = (7-5)/(2-1) = 2
Choose b so that y = 2x + b goes through either point.

7 = 2*2 + b

Solve for b and then write the standard equation with numbers substituted for m and b