There are three main ways that you can write an equation. Those are general form, point slope, and slope Y intercept.
General Form
General Form tells you nothing about the equation and is known as pretty useless. General form will always equal zero and the first coefficient will always be positive or it is incorrect. There can also not be any fractions in the equation or it is also in correct. Fir example 2x-y+5=0 is an example of general form because it has no fractions, it equals zero, and the first coefficient is positive. The equation -2x-y+4=-1 is not general form because the first coefficient is a negative and it does not equal zero. To make it general form you will need to move everything to the other side making the equation 0=2x+y-5.
Slope Y intercept
Slope Y intercept is the equation y=mx+b. In this equation it tells you the slope and the y intercept. The mx is the slope and the b is the y intercept. This means that you will be able to graph a line using this formula. For example if the equation is y=2x+2 you know that the y intercept is two so you start at 2 and go up 2 and one to the right because it is positive.
Point slope
Point slope is the equation m(x-x)=y-y. You use this formula when you are given coordinates and need to put them into an equation. For example if you are given the coordinates (3,1) and (6,2) we can make an equation. The equation would be 3(x-3)=y-1. This is the equation because we known the slope is 3 because of the difference in the coordinates and the slope will go in front of the brackets. You then insert the x and y coordinates into the equation making it -3 and -1 because a positive and a negative = a negative.