AI Tutor
Imagine you have exactly 30tospendonsnacksatamovietheater.Ifpopcorncosts30 to spend on snacks at a movie theater. If popcorn costs 5 and sodas cost $3, how many of each can you buy?
If xx is the number of popcorns and yy is the number of sodas, the total cost gives us 5x+3y=305x + 3y = 30. This clean balance between two items is the power of standard form.
Most linear equations you meet start in other formats — so what exact rules make an equation truly in standard form?

The Three Rules of Standard Form

The standard form of a linear equation is written as Ax+By=CAx + By = C, where xx and yy are variables and AA, BB, and CC are fixed numbers.
To be officially in standard form, your equation must follow three strict rules: AA, BB, and CC must be integers (no fractions or decimals), AA must be positive (A≥0A \ge 0), and the greatest common factor of AA, BB, and CC must be 1.
What if you are handed a slope and a yy-intercept instead? Let's see how we convert that into standard form.

Writing Standard Form from Slope and Intercept

Suppose a line has a slope of m=−34m = -\frac{3}{4} and a yy-intercept at (0,2)(0, 2). In slope-intercept form, this is y=−34x+2y = -\frac{3}{4}x + 2.
To clear the fraction, multiply every single term by the denominator 44, which gives 4y=−3x+84y = -3x + 8.
Next, add 3x3x to both sides to group the xx and yy terms together on the left: 3x+4y=83x + 4y = 8. Since A=3A = 3 is positive and all coefficients are integers with a common factor of 1, we are done!