Question

Given a graph of a function, explain how to find the rate of change and how to determine whether it is a linear or nonlinear function.

Answer 1

Answer:

To see if a table of values represents a linear function, check to see if there's a constant rate of change. If there is, you're looking at a linear function! This tutorial shows you how to tell if a table of values represents a linear function.

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Answer 2

The slope of the graph gives the rate of change of variable 'y' with respect to variable 'x'.

• The slope of a graph is given by Δy/Δx or dy/dx.
• This quantity gives the rate of change of y with changes in x.
• If the slope is positive, 'y' increases as 'x' increases.
• If the slope is negative, 'y' decreases as 'x' increases.
• If the slope is 0, 'y' remains constant irrespective of change in 'x'.
• To determine if the function is linear, check Δy/Δx. If the change is directly proportional to the previous change then the function is linear.