The General Procedure

1. Subtract mx From Both Sides

\begin{aligned} y - mx &= (mx - mx ) + b \\ y - mx &= b \end{aligned}

2. Subtract b From Both Sides (Optional)

\begin{aligned} y - mx - b &= b - b \\ y - mx - b &= 0 \end{aligned}

3. Rearrange to Put the x Term First

-mx + y - b = 0

4. Let the Fraction A/B Represent m

If m is an integer, then B will equal 1.

-\frac{A}{B}x + y - b = 0

5. Multiply Both Sides of the Equation by the Denominator B

-Ax + By - Bb = 0

6. Let Bb = C

-Ax + By - C = 0

Examples:

1. Subtract 1/2 x From Both Sides of the Equation

y - \frac{1}{2}x = 5

2. Subtract 5 From Both Sides

y - \frac{1}{2}x - 5 = 0

3. Multiply Both Sides by the Denominator of the Fraction

2y - x - 10 = 0

4. Rearrange to Put x as the First Term

-x + 2y - 10 = 0

You can leave the equation like this, but if you prefer to make x positive, multiply both sides by -1:

x - 2y + 10 = 0

or

x - 2y = -10

(2) - The slope of a line is -3/7 and the y-intercept is 10. What is the equation of the line in standard form?

The slope intercept form of the line is

y = -\frac{3}{7}x + 10

Following the procedure outlined above:

\begin{aligned} y + \frac{3}{7}x - 10 = 0 \\ 7y + 3x - 70 = 0 \\ 3x + 7y -70 = 0 \\ \text{or} \\ 3x + 7y = 70 \end{aligned}