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.



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

y = mx + b

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

the difference in the y-coordinated divided by the difference in the x-coordinates.

Thus for your example

m = [5 - 7]/[0 -(-3)]-2/3

Thus, so far the equation of the line is

y = -2/3 x + b

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

5 = -2/3 (0) + b

Hence b = 5 and the euqation of the line is

y = -2/3 x + 5

Your form has the x and y terms on the left of the equal sign so add  2/3 x to bothsides to get

y + 2/3 x= -2/3 x + 5 + 2/3 x or

 2/3 x + y =  5

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

3 2/3 x + y) =  3 5


2x + 3y = 15



Go to Math Central