Question

How can you change linear equation in form ax+by=c to y=mx+b form and vice versa

Answer 1

You simply have to take the linear equation form (ax + by = c) and solve for y. So you get:
by = c - ax
y = c/b - ax/b

Since c/b will be a constant, you can replace it with any variable (i.e. b), and so that represents the y-intercept and a/b will also be a constant, so that can also be replaced by any variable (i.e. m), and it represents the slope.