5.5 Standard Form of a Linear Equation

Mrs. Agriesti's Algebra

Goal: To learn to transform a linear equation into standard form.

Slope-intercept form:     y = mx + b

Standard form:               Ax + By = C

Examples:  Write each equation in standard form with integer coefficients.

    y = (3/4)x + 2
  4y = 3x + 8
  -3x + 4y = 8

First, multiply by 4 to clear the equation of fractions.

Then move the 3x to the left side of the equal sign (make sure to change the sign when you cross over)

    y = -3x - (5/8)
  8y = -24x - 5
  24x + 8y = -5

First, multiply by 8 to clear the equation of fractions.

Then move the -24x to the left side of the equal sign (make sure to change the sign when you cross over)

    y = -0.23x + 5.2
  100y = -23x + 520
  23x + 100y = 520

First, multiply by 100 to clear the equation of decimals.

Then move the -23x to the left side of the equal sign (make sure to change the sign when you cross over)

    1.5y = 3 - 1.11x
150y = 300 - 111x
111x + 150y = 300

First, multiply by 100 to clear the equation of decimals.

Then move the -111x to the left side of the equal sign (make sure to change the sign when you cross over)

(2/5)y = 3x - 1/3
     6y = 45x - 5
-45x + 6y = -5
  45x - 6y = 5

First, multiply by 15 to clear the equation of fractions.

Then move the 45x to the left side of the equal sign (make sure to change the sign when you cross over)

Distribute a negative to make the coefficient of x positive.