Final answer:
To convert an equation from slope-intercept form (y = mx + b) to standard form (Ax + By = C), subtract mx from both sides, clear any fractions, and adjust the equation so that A is a positive integer.
Step-by-step explanation:
To convert a linear equation from slope-intercept form to standard form, you can follow these general steps:
- Start with the slope-intercept form of the equation, which is typically written as y = mx + b where m is the slope and b is the y-intercept.
- Rearrange this equation to get the x and y variables on one side of the equation. This often involves subtracting mx from both sides to give y - mx = b.
- Now you need to get rid of any fractions, so if your equation includes fractions, multiply all terms by the denominator to clear them.
- Finally, standard form is typically written as Ax + By = C, where A, B, and C are integers, and A is non-negative. If A is negative, you can multiply the entire equation by -1 to make it positive.
As an example, let's convert the slope-intercept equation y = 3x + 9 to standard form. We can subtract 3x from both sides to get -3x + y = 9. Then, if we want A to be positive, we can multiply through by -1 to get 3x - y = -9, which is now in standard form.
In another example, if your equation is y = 55x + 75, subtracting 55x from both sides yields -55x + y = 75. Multiplying through by -1, the equation in standard form becomes 55x - y = -75.