Question

Which equation is represented by the table?

Answer 1

`y=-|x-3|-3`

Explanation:

The table shows values of
`y` for different values of
`x`.

Let us test each equation with the values given in the table.

Equation 1:
`y=|x+3|-3`

For
`x` = 1, we get,

`y=|x+3|-3=|1+3|-3=|4|-3=4-3=1`

So, we got 1 for
`y`. But as per table, value of
`y` should be -5.

So, equation 1 is incorrect.

Equation 2:
`y=-|x-3|-3`

For
`x` = 1, we get,

`y=-|x-3|-3=-|1-3|-3=-|-2|-3=-(2)-3=-5`

So, we got -5 for
`y`. It matches with the value of table.

Let us check for another value of
`x` in order to confirm.

For
`x =2`, we get,

`y=-|x-3|-3=-|2-3|-3=-|-1|-3=-(1)-3=-4`

So, we got -4 for
`y`. It matches with the value of table.

So, equation 2 is the correct answer.

We can be completely sure by checking the remaining equations too.

Equation 3:
`y=|x-3|-3`

For
`x` = 1, we get,

`y=|x-3|-3=|1-3|-3=|-2|-3=2-3=-1`

So, we got -1 for
`y`. But as per table, value of
`y` should be -5.

So, equation 3 is incorrect.

Equation 4:
`y=-|x+3|-3`

For
`x` = 1, we get,

`y=-|x+3|-3=-|1+3|-3=-|4|-3=-4-3=-7`

So, we got -7 for
`y`. But as per table, value of
`y` should be -5.

So, equation 4 is incorrect.