Help Maths Question! Please Reply Soon?

Question

The point A and B have coordinates (a,a2) and (2b,4b2) respectively. Determine the gradiant of AB in its simplest form.

Answer 1

Okay, first, gradient is just the same thing as slope, right? So, you just use the formula to find slope which is:

m = y2-y1

     ----------

      x2-x1

point A is (x1,y1) or (a,a2)  

point B is (x2,y2) or (2b,4b2)

Now we just plug it in =]

y2-y1  =   (4b2) - (a2)

---------      -------------------

x2-x1        (2b)  -  (a)

Next, we can't actually subtract these, because it's different variables. But, what we can do is simplify.

Let's try breaking these up.

(4b)2                                                                

--------

  2b

you can divide each by 2

2b2

-------

    b                                                                

Next, we can divide the b2 and the b by b

2b (over 1)

Now, let's do the other side.  

   a2

--------

    a

We can divide a2 & a by a.

       a (over 1)

Now we can put both sides back together and it would be:

m = 2b - a.

I know it looks kind of confusing, but it's hard to type it out >_<

Answer 2

gradient (m) = (y2 - y1) / (x2 - x1)

= [(4b^2) - (a^2)] / (2b - a)

Factorising (4b^2) - (a^2):

(4b^2) - (a^2) = (2b + a) (2b - a)

Putting it back into the gradient equation:



m = [(2b + a) (2b - a)] / (2b - a)

Therefore, m = 2b + a