Any equation that relates the first power of x to the first power of y produces a straight line on an x-y graph. The standard form of such an equation is Ax + By + C = 0 or Ax + By = C. When you rearrange this equation to get y by itself on the left side, it takes the form y = mx +b. This is called slope intercept form because m is equal to the slope of the line, and b is the value of y when x = 0, which makes it the y-intercept. Converting from slope intercept form to standard form takes little more than basic arithmetic.
To convert from slope intercept form y = mx + b to standard form Ax + By + C = 0, let m = A/B, collect all terms on the left side of the equation and multiply by the denominator B to get rid of the fraction.
An equation in slope intercept form has the basic structure
\begin y - mx &= (mx - mx ) + b \\ y - mx &= b \end \begin y - mx - b &= b - b \\ y - mx - b &= 0 \end -mx + y - b = 0If m is an integer, then B will equal 1.