How was the following Algebra equation rearrangd?

Question

How is the formula: (y-b) / (0-b) = (x-0) / (a-0) rearranged to: x / a + y / b = 1 ? Thanks in advance.

Answer 1

Given (y-b) / (0-b) = (x-0) / (a-0), we can simplify to (y-b)/(-b) = x/a.

 

Or x/a + (y-b)/b = 0.  Or x/a + y/b - 1 = 0 [applying denominator b to both y and -b] and then finally to x/a + y/b =1.

 

This happens to be the equation of a st. line having x-intercept a and y-intercept b.  

 

It's quite a useful formula, often not taught nowadays.