Question

The table below shows the relationship between feet and yards fill in each box to write an algebraic expression to a represent the number of feet and any number of yards

Answer 1

We are asked to write an algebraic equation to represent the number of feet in any number of yards:

Words:

Clearly from the entries in the table we could say that:

The number of feet is three(3) times the number of yards.

Variable:

Let f denotes the number of feet.

and y denotes the number of yards.

Model:

So, finally we could write our algebraic equation in terms of variables as:

`y=(1)/(3)f`

Answer 2

The Direct Variation says that:

`y \propto x`

Then; the equation becomes:
`y =kx` where k is the constant of variation.

Let y represents the number of feet and f(y) represents the number of yards.

then;

by definition of direct relationship we have;

`f(y) = ky`

Substitute any values from the given tables to solve for k;

Let y = 3 and f(y) = 1

then;

`1 = 3k`

Divide both sides by 3 we get;

`k = (1)/(3)`

then, the model of the equation becomes:
`f(y) = (1)/(3)y`

In Words :
`(1)/(3)` times the number y.

Variable : Let y represents the number of feet.

Model :
`f(y) = (1)/(3)y`

An algebraic expression to represents the number of feet in any number of yards,
`f(y) = (1)/(3)y`