For week 16 in Math 10, we are once again continuing on learning about linear equations and expanding our knowledge on how to deal with lines, graphs, and of course equations. This week, we focused mainly on three different ways we can write an equation for a line/line segment. So for this post, I will teach you/remind myself how to write out these equations, and how to convert one to the other.
First before we begin, we once again need to know the basics to this subsection of the unit. There are three equations that we have learned to plot a line. They are Slope Intercept Form (y = mx + b), General Form (Ax + By + C = 0), and Point Slope Form (m(x – x1) = y – y1). My favorite is Slope intercept form because it gives us the most data from looking at it (We will get into that in a sec) however it takes longer to write out as oppose to the easier and quicker form which is Point Slope Form. Point Slope Form is most people’s favorite as it requires less time to write out compared to Slope Intercept and General Form. The last form is nobody’s favorite; General form. This is the least liked because it is not very convenient as you cannot write it out without converting another form into is as well as a few other flaws that I will get into. Lastly before we dive deeper into these forms, I do want to mention two things more things. First, it is important to know that you only require two pieces of information to determine the equation of the line, one of which has to be the slope or a way to find the slope. Second, it does not matter which form you use and it only matters which you prefer the most because all of these forms are EXACTLY EQUIVALENT.
Slope Intercept Form (y = mx + b) is probably the best form when it comes to the data that it gives us. It is probably the most useful because we learn the slope (mx) of an equation as well as the y intercept that the line passes through (b). The only detriment to this is that it takes longer to write down than the Point Slope form so it is less efficient.
So to begin our is to write the equation of a line that has the same y intecept as y = 2x – 3 and is perpendicular to y = 
Next we are going to learn how to write down an equation using the Point Slope Form (m(x – x1) = y – y1). 
Like earlier stated, this is most people’s favorite as it is the most efficient to to quickly write down and we know the Slope as well (m). However, it’s only detriment is that it does not tell us the y intercept so it does not give us as much information as the Slope Intercept Form. So to write an equation using this form, we only need the slope, and the coordinates of only one point. For our example we are going to state the equation knowing that 4 is our slope and the coordinates are (9, 3). So for this one, it is super easy because all we need to do is to place the slope and the coordinates into the equation. Because our slope is 4 than we can replace m getting 4(x – x1) = y – y1. Next all we need to do is place the coordinates (9, 3) into the equation. The x1 and y1 is where we are going to place our x and y variables respectively and in the end we will end up with 4(x -9) = y -3.
Lastly we are going to learn how to write an equation using General Form (Ax + By + C = 0). This is the last used and least like form because we cannot write it without converting slope intercept form into it , It does not give us any information telling us the slope, y intercept, or a coordinate, and there are so many rules for this form. 
First, the leading coefficient (Ax) has to be positive for this to work. Next, one side of the equation has to = 0. And lastly, all of the coefficients (A, B, and C) have to be integers for this to work. So for our example, we are going to learn how to convert Slope Intercept Form into General Form. For this example, we need to convert y = 
