Definition: Standard form writes a linear equation as Ax + By = C, with A, B, and C integers and A not negative, which makes both intercepts easy to find.
What does Ax + By = C look like?
The x-term and y-term sit on the left and the constant sits on the right, as in 6x + 4y = 24. Many textbooks ask for A, B, and C to be whole numbers with no common factor, and for A to be positive.
Why use it?
It is the quickest form for intercepts. Set y = 0 to get the x-intercept, and set x = 0 to get the y-intercept. It also suits problems with two quantities adding up to a total, such as tickets and snacks sold for a fixed budget.
Example. For 6x + 4y = 24, setting y = 0 gives x = 4, and setting x = 0 gives y = 6. The line crosses the axes at (4, 0) and (0, 6). Dividing by 2 gives the simplest standard form, 3x + 2y = 12.
How do you find the slope?
The slope is -A/B. For 3x + 2y = 12 the slope is -3/2. A frequent error is dropping the minus sign. If you are unsure, solve for y and read the coefficient of x.
Where to learn it
- Writing and Graphing Linear Functions in Three Forms – lesson
- Solving Linear Equations and Rearranging Formulas – lesson