Question

There are 4 quarters in 1 dollar. The total number of dollars is a function of the number of quarters. Does this situation represent a linear or nonlinear function? Explain why.

Answer 1

A Linear function because the slope is constant.
If dollars represents the "y value" and quarters the "x value"
Then slope = rise/run = 1/4

$y = \frac{1}{4} x$

Answer 2

If you make a table of values, you can see that 4 quarters equal 1 dollar and 8 quarters equal 2 dollars. If you graph the data, you will see a straight line. Therefore, this situation represents a linear function with a constant rate of change of 1/4.