This week we learned how to change an equation from point slope form to general form. Point slope form is where the equation should look like this: m(x-x)=y-y. This form is useful because it gives a lot of information about the equation. You can immediately see the slope of the equation (slope = m) , the ordered pair being used (the second x and y variables would be the coordinates) and it can be rearranged easily to other forms like general form and slope y intercept form. General form is not very useful but you can easily tell if the equation is linear by seeing if the highest degree is 1 (making sure the variable has no exponents higher than 1). General form must only include integers (no fractions) it’s leading coefficient must be positive and the equation must equal to 0. To change point slope form to general form you can follow the steps and use the equation 9(x-2)=y-3.
1. Add 3 on both sides of the equal sign. Our goal is to get the equation equal to 0 so we start getting rid of the y and the -3. The equation should now look like this: 9(x-2)+3=y.
2. Simplify the equation. Use distributive law to simplify the 9(x-2) so that it becomes 9x-18+3=y. Then, simplify it further by adding the -18 and 3. It should then look like this: 9x-15=y.
3. Subtract y from both sides of the equal sign. We do this to make the equation equal 0 by cancelling out the y on the right side. The y should go right after the x value. Your final answer should be: 9x-y-15=0.
As long as you remember your algebra, distributive property and BEDMAS you should be able to use these steps to rearrange a variety of equations into general form.