Question

Part A: A graph passes through the points (0.2). (1.3), and (2, 4). Does this graph represent a linear function or a non-linear function? Explain your answer in

words
Part 3: Write one example of a linear function and one example of a non-linear function (Use x and y as the variables)

Answer 1

a) Linear because there is a constant slope

b) Linear: y=x

Non-linear: y=1/x

Explanation:

First we find the slope using the formula:

`m = (y_2-y_1)/(x_2-x_1)`

For the points (0,2) and (1,3), we have

`m = (4-3)/(1-0) = (1)/(1) = 1`

For the points (0,2) and (2,4), we have

`m = (4 - 2)/(2 - 0) = (2)/(2) = 1`

For (1,3) (2,4), we have;

`m = (4 - 3)/(2 - 1) = 1`

Since there is a constant rate of change the graph represents a linear function.

b) For a linear function, the highest degree is 1.

An example of a linear function is y=2x

For a non-linear function the degree of the variable is not equal to 1.

`y = (1)/(x)`