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Math P2 MJ 2010 doubts

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Arthur Bon Zavi:
For The 15th one:

(a). See the pattern (sequence):

Y co-ordinates are 5, 3 and 1. Means -2 every time, i.e 5-2=3, then 3-2=1.
X co-ordinates are 2, 3 and k. This also has the sequence, i.e 2+1=3, then 3+1=4, so k(x co-ordinate)=4.

(b).
For the Gradient remember the formula:

y2-y1
-------
x2-x1

The Points are, (2,5), (3,3) and (4,1).

take any two points, e.g (2,5) and (3,3).

then:

3 - 5      -2
------ = ----- = -2
3 - 2       1

Gradient (Slope)= -2.

m = gradient = slope = -2.

so:

y=mx+c.
put any of the values.

3=-2*3+c

so,
c=9.

so equation goes:

y=-2*x+9

Or a simpler method if u have gradient, then:

y-y1=m(x-x1), where m is gradient (slope).

Example from this:

y-3=-2(x-3)
y-3=-2x+6
therefore: y=-2x+9. [It's Easy].

Another Method is when u don't have a gradient and have atleast two co-ordinates, so here u have 3 (more than necessary).  :D

take any two:

like (2,5), and (3,3).

Equation is :

y-y1      x-x1
-----  = ------
y2-y1    x2-x1

so, by substituting:

y -5     x - 2
----- = ------
3 -5     3 - 2

It gives:

y -5 = -2 (x - 2)
y - 5 = -2x+4
y = -2x + 9

Arthur Bon Zavi:
This answer I just explained briefly with the help of alternative known methods, and other answers are explained by Ari.
 ;)

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