How Do You Convert From Slope Intercept to Standard Form?

Many linear equations are given in slope-intercept form (y = mx + b), and sometimes they must be converted to standard form (Ax + By = C). Converting slope-intercept to standard form is mostly a matter of converting fractions to integers and can be done on paper in a couple minutes.

  1. Determine what terms to change

    In many y = mx + b equations, the slope (m) or the y-intercept (b) is often given in a fraction. Sometimes both are. The fractions must be changed to integers in standard form. For example, if the equation is y = (3/4)*x + 2, the 3/4 must be changed. If the equation is y = 2x + 7/2, the 7/2 must be changed.

  2. Cancel out the denominators

    When canceling terms, make sure you perform the same operation on both sides of the equation. For the equation y = (5/2)*x + 4/3, both 5/2 and 4/3 need to be cancelled out. To cancel a denominator of 2, multiply by a numerator of 3; to cancel a denominator of 3, multiply by a numerator of 3. 2*3*y = 2*3*((5/2)*x + 4/3) 6y = 6((5/2)*x + 4/3) 6y = 3*5*x + 2*4 6y = 15x + 8

  3. Isolate the constant

    In the equation 6y = 15x + 8, 8 is the constant. To isolate it, subtract 15x from both sides. 6y - 15x = 15x + 8 - 15x 6y - 15x = 8