Question

3. (04.04 MC)

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 B: Write one example of a linear function and one example of a non-linear function.. (Use x and y as the variables) (10 points)

Answer 1

Part A:

The graph passes through (0,2) (1,3) (2,4).

If the graph that passes through these points represents a linear function, then the slope must be the same for any two given points. Using (0,2) and (1,3). Write in slope-intercept form, y=mx+b. y=x+2

Using (0,2) and (2,4). Write in slope-intercept form, y=mx+b. y=x+2. They are the same and in graph form, it gives us a straight line.

Since the slope is constant (the same) everywhere, the function is linear.

Part B:

A linear function is of the form y=mx+b where m is the slope and b is the y-intercept.

An example is y=2x-3

A linear function can also be of the form ax+by=c where a, b and c are constants. An example is 2x + 4y= 3

A non-linear function contains at least one of the following,

*Product of x and y

*Trigonometric function

*Exponential functions

*Logarithmic functions

*A degree which is not equal to 1 or 0.

An example is...xy= 1 or y= sqrt. x

An example of a linear function is 1/3x = y - 3

An example of a non-linear function is y= 2/3x