Question

The table shows a familiar pattern from geometry. Determine what the variables $\mathrm{x}$ and $\mathrm{y}$ represent. Then write a function rule that relates $\mathrm{y}$ to $\mathrm{x}$.

Is the function a linear function?

Answer 1

We know if the power of $\mathrm{x}$ and $\mathrm{y}$ is $1$ then function is linear.

Here, $\mathrm{x}$ is is diameter of circle and $\mathrm{y}$ is the circumference.

We know, Area of circle $\mathrm{y}=\mathrm{\pi d}$ where (diameter) $\mathrm{d}=\mathrm{x}$ given.

Thus, function rule: $\mathrm{y}=\mathrm{\pi x}$

As the power of $\mathrm{x}$ and $\mathrm{y}$ is $1$ therefore, function is linear.

Hence, the given function is linear.