Question

What is the rule for this table? x y 9 2 12 333 1042 13 y= ------- x-

Answer 1

We get the two points (9,2) and (12,3) from the table.

Consider the equation

`y=mx+b`

Substitute x=9 and y=2, we get

`2=m(9)+b`
`b=2-9m`

Substitute x=12 and y=3 in the equation, we get

`3=m(12)+b`

Substitute b=2-9m to find the value of m.

`3=12m+2-9m`

`3-2=3m`
`m=(1)/(3)`

Substitute m=1/3 in b=2-9m to find the value of b.

`b=2-9((1)/(3))`

`b=-1`

Substitute m=1/3 and b=-1 in the equation, we get

`y=(1)/(3)x-1`

Verification:

consider the third point (33,10).

Substitute x=33 and b=10 in the equation, we get

`10=(1)/(3)*33-1`

`10=11-1`

`10=10`

It is verified.

Hence the required equation is

`y=(1)/(3)x-1`