Question

The number of trees (n) that the average American uses in paper products varies directly with the time (t) in years. Assume that the constant of proportionality is 7. Write an equation that represents the proportional relationship between n and t using the given information.

Answer 1

`n=7t`.

Explanation:

1. Theory.

Linear equations are those that contain constants of proportionality, and they have the following form:

`y=mx+b`; where "m" represents the constant of proportionality and "b" is the y-intercept.

2. Form the equation.

We are being asked to make a function whose n value (number of trees) varies directly with time (t). This means that the independent variable is time, because it determines the number of trees. Hence, we know that "t" is going to be our "x" value and "n" is going to be our "y". Finally, we know that the constant of proportionality "m" is 7.

Edit the previously presented model and adapt it to this case:

`y=mx+b\\ \\n=7t`

Note: The value of the y-intercept was removed since the problem didn't give a value for it.

3. Present the equation.

`n=7t`; where "n" is the number of trees that the average American uses in paper products and "t" is time in years.