Question

If y= 2 2/3 when x= 1/4, find y when x= 1 1/8

Answer 1

Value of y when x =
`1 (1)/(8)` is y = 12

Step-by-step explanation:

In order to find different values of y for different values of x, we need to develop equation of y in terms of x.

Let us assume
`y = m * x + c`, where m is slope and c is constant.

Substituting values of
`y = 2 (2)/(3)` and
`x = (1)/(4)` in the assumed Equation:

`y = m * x + c`

`2 (2)/(3) = m *  (1)/(4) + c`

`(8)/(3) = m *  (1)/(4) + c`

In order to equate the equation, c needs to be zero, because for any other value of c except zero, the equation would not equate.

`(8)/(3) = m *  (1)/(4)`

`m = ((8)/(3) )/((1)/(4) )`

`m = (8 * 4)/(3 * 1)`

`m =(32)/(3)`

Substituting value of m in the assumed equation,

`y = (32)/(3) * x`

Now when x =
`1 (1)/(8)` =
`(9)/(8)`

`y = (32 * 9)/(3 * 8)`

`y = 4 * 3 = 12`