Quandaries and Queries
I was wondering if you could please explain to me how I would write the equation of line through the given points [(-3,7), (0,5)] in Ax+By=C form.
I am a GCSE student in year 11. Please answer as soon as possible.
There are a number of ways to arrive at the equation in the form you want. I will show you what is probably the most common way. I am going to write the equation in the form
and then convert to the form that you want.
In the form above m is th slope of the line. That I calculate first as
Thus for your example
Thus, so far the equation of the line is
Since both points (-3,7) and (0,5) lie on the line they each satisfy the equation of the line. Thus substitute the coordinates either point into the equation. I'm going to substitute (0,5) and I get
Hence b = 5 and the euqation of the line is
Your form has the x and y terms on the left of the equal sign so add 2/3 x to bothsides to get
Thi is of the form you requested but I would simplify it even more by multiplying both sides by 3 to eliminate the fraction. Thus I get