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

or

2x + 3y = 15

Penny

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