SOLUTION: i am having trouble with finding the rule for the function x y 0 3 2 4 4 5 6 6 i have trouble in general with every problem but this is the one im really stuck

Question 210183: i am having trouble with finding the rule for the function
x y
0 3
2 4
4 5
6 6
i have trouble in general with every problem but this is the one im really stuck on! thanks
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's assume that there is a linear relationship. So this means that there's a line that goes through every point listed above.

To find the equation of the line, we only need two points. So let's use (0,3) and (2,4)

First let's find the slope of the line through the points

and

Note:

is the first point

. So this means that and .
Also,

is the second point

. So this means that and .

Start with the slope formula.

Plug in , , , and

Subtract from to get

Subtract from to get

So the slope of the line that goes through the points

and

is

Now let's use the point slope formula:

Start with the point slope formula

Plug in , , and

Distribute

Multiply

Add 3 to both sides.

Combine like terms.

So the equation that goes through the points

and

is

This line also goes through the other points listed above.

Note: To make a function, simply replace 'y' with 'f(x)' to get

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