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.
TL;DR (Too Long; Didn't Read)
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.
The General Procedure
An equation in slope intercept form has the basic structure
Subtract mx From Both Sides
Subtract b From Both Sides (Optional)
Rearrange to Put the x Term First
Let the Fraction A/B Represent m
Multiply Both Sides of the Equation by the Denominator B
Let Bb = C
If m is an integer, then B will equal 1.
(1) - The equation of a line in slope intercept form is:
What is the equation in standard form?
Subtract 1/2 x From Both Sides of the Equation
Subtract 5 From Both Sides
Multiply Both Sides by the Denominator of the Fraction
Rearrange to Put x as the First Term
You can leave the equation like this, but if you prefer to make x positive, multiply both sides by -1:
(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
Following the procedure outlined above: