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Write a rule for a function table

Write the rule for the following function table.

 y=______ 7 13 4 10 9 15 2 8 5 11 6 12

The solution is y=x+6

Write the rule for the following function table.

 y=______ 1 0 2 1 3 2 4 3

Linear functions are of the form y=mx+b.

1. First find m.
Look at the table and notice that every time the terms x go up by 1, the y terms go up by 1. This means that m is equal to 1.

2. Next find b.
Take the equation y=mx+b and plug in the m value (m=1) and a pair of (x,y) coordinates from the table, such as (1,0). Then solve for b.

 y = mx+b 0 = 1(1)+b Plug in m=1, x=1 and y=0 0 = 1+b Simplify -1 = b Simplify

3. Finally, use the m and b values you found (m=1 and b=-1) to write the equation.

 y = mx+b y = 1x-1 Plug in m=1 and b=-1 y = x-1 Simplify

So, the equation is y=x-1