Quandaries
and Queries 

Farzana 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. 

Hi Farzana, 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
or
Penny 

