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

Answer

a) Linear because there is a constant slope

b) Linear: y=x

Non-linear: y=1/x

Step-by-step explanation:

First we find the slope using the formula:

$m = \frac{y_2-y_1}{x_2-x_1}$

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

$m = \frac{4-3}{1-0} = \frac{1}{1} = 1$

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

$m = \frac{4 - 2}{2 - 0} = \frac{2}{2} = 1$

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

$m = \frac{4 - 3}{2 - 1} = 1$

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.

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