1. The problem is to explain the concept of standard form in mathematics. 2. Standard form can refer to different things depending on the context, but commonly it means writing numbers or equations in a specific, widely accepted way. 3. For numbers, standard form often means writing a number as a product of a number between 1 and 10 and a power of 10, also called scientific notation. For example, the number 4500 in standard form is written as $$4.5 \times 10^3$$. 4. For linear equations, the standard form is usually written as $$Ax + By = C$$, where $$A$$, $$B$$, and $$C$$ are integers, and $$A$$ and $$B$$ are not both zero. 5. Important rules for standard form of linear equations: - $$A$$ should be a non-negative integer. - $$A$$, $$B$$, and $$C$$ should be simplified so they have no common factors other than 1. 6. Example: Convert the equation $$y = 2x + 3$$ to standard form. 7. Start by rewriting the equation: $$y = 2x + 3$$ 8. Move all terms to one side: $$-2x + y = 3$$ 9. Multiply both sides by $$-1$$ to make $$A$$ positive: $$\cancel{-1}(-2x + y) = \cancel{-1}(3)$$ $$2x - y = -3$$ 10. The equation in standard form is $$2x - y = -3$$. This is the standard form of the linear equation. In summary, standard form is a way to write numbers or equations clearly and consistently, making them easier to understand and work with.