Question

The relationship between Sergio's age and Fernando's age is illustrated in the graph. Are their ages proportional? Is the relationship an example of direct variation? Why or why not?

Answer 1

The graph we are told, shows the relationship between two variables which are, Sergio's age and Fernando's age.

Note that the graph slopes upwards which means as one value increases, the other one also increases. we shall calculate the slope as follows;

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ \text{When Fernando is 1, Sergio is 3. That is }(1,3) \\ \text{When Fernando is 2, Sergio is }4.\text{ That is}(2,4) \\ m=(4-3)/(2-1) \\ m=(1)/(1) \\ m=1 \end{gathered}`

We can compare this result with another set of ages (ordered pair) as follows;

`\begin{gathered} \text{When Fernando is }3,\text{ Sergio is 5. That is}(3,5) \\ \text{When Fernando is 4, Sergio is 6. That is }(4,6) \\ m=(6-5)/(4-3) \\ m=(1)/(1) \\ m=1 \end{gathered}`

The rate of change is the same for both of them at every point which means their ages are directly proportional.

ANSWER:

This relationship is an example of direct variation because as Fernando's age increases, Sergio's age also increases and the rate of increase is the same at any point on the graph