How do I convert y=Mx+b into standard form using integers?

Answer 1

The slope-intercept form of the equation of a line looks like: y=mx+b

The Standard Form of the equation of line looks like: Ax + By = C

This problem: y=Mx+b

-Mx + y = b

Mx - y = -b [note: By convention, coefficient of x is positive integer]

If M is not a positive integer, then there is a integer value N that makes MN a positive integer;

the denominator, if M is a fraction]

MNx - Ny = -Nb

Answer 2

since y = M·x + b

so M·x - y + b = 0

if M and/or b are not integers, you can always convert them into fractions as long as they are rational numbers. For example: M = m₁/m₂, and b=b₁/b₂,

so we have (m₁/m₂) x - y + b₁/b₂ = 0

and we can get a standard form using integers as: m₁b₂·x - m₂b₂·y + m₂b₁ = 0 .