One concept I found challenging this week was changing an equation into general form. There is a lot of rearranging involved.

Ex. 2/3x – 7=1/2y

There are a few rules for general form. The format for the form is Ax+By+C=0. All of the input numbers have to be integers and the A number has to be a positive.

The first thing we are going to do is find the common denominator for 1/2 and 2/3 in order to change the fractions into integers. This number is 6. We will multiply all of the numbers by 6. 1/2, 2/3 and -7  will then become 6/2, 12/3 and -42. The fractions can be simplified into 3 and 4 when divided. The new expression is now 4x-42=3y.

Now that all the numbers are integers and A (x value) is positive, we have to rearrange the equation from point slope form into general form.

We will put 0 on the right side because, whenever a value moves from one side to another, it changes from positive to negative or vice-versa and our   A value is already positive on the right side so, we don’t want to change that.

4x-3y-42=0 is our final equation. As you can see, the 3y turned negative because it got switched from the right side to the left side.