How to Change Between Slope-Intercept Form and Standard Form

Changing equations from slope-intercept form ($y = mx + b$) to standard form ($Ax + By = C$) can be tough for many students.

This is because the way the equation looks changes, which makes it hard to see important parts like the slope and intercepts.

How to Change from Slope-Intercept Form to Standard Form:

1. Start with the slope-intercept equation: $y = mx + b$.

2. Move $mx$ to the other side. This gives you: $-mx + y = b$.

3. If you want $A$ to be positive, multiply the whole equation by -1. Now you have $Ax + By = C$.

How to Change from Standard Form to Slope-Intercept Form:

1. Start with the standard form: $Ax + By = C$.

2. Solve for $y$. This means rearranging it to get: $By = -Ax + C$.

3. Divide everything by $B$: $y = -\frac{A}{B}x + \frac{C}{B}$. Now you can see the slope and intercept clearly.

With practice, you can get better at this! Consistency is key to making it easier.