# finding the equation that relates to set of two numbers

• Oct 7th 2009, 10:18 PM
nicotynamide
finding the equation that relates to set of two numbers
can someone help me find the equation that relates to these sets of paired numbers and plz explain the method used

0 - 2
1 - 4
2 - 6
3 - 8
4 - 10
• Oct 7th 2009, 10:42 PM
mr fantastic
Quote:

Originally Posted by nicotynamide
can someone help me find the equation that relates to these sets of paired numbers and plz explain the method used

0 - 2
1 - 4
2 - 6
3 - 8
4 - 10

y = 2x + 2.

(If you plot the points it's obvious there is a linear relationship y = mx + c. When x = 0, y = 2 so c = 2. Then y = mx + 2. And the gradient is easily seen to be m = 2).
• Oct 7th 2009, 10:56 PM
pacman
since this is a linear equation, use point-slope form of line: y = mx + b

@(0,2), then

2 = m(0) + b, then b = 2.

Next, @ (1,4) and b = 2,

4 = m(1) + 2,

m = 4 - 2, then

m = 2, this your slope which is m.

Now you know your y-intercept, b which is equal to 2 and slope m, which is equal to 2.

y = 2x + 2,

CHECK: @ x = 0, 1, 2, 3, 4, we have

y = 2(0) + 2 = 0 + 2 = 2,
y = 2(1) + 2 = 2 + 2 = 4,
y = 2(2) + 2 = 4 + 2 = 6,
y = 2(3) + 2 = 6 + 2 = 8,
y = 2(4) + 2 = 8 + 2 = 10.

We now confirmed the correctness of our generated equation y = 2x + 2.