Question

Part A: A graph passes through the points (0, 2), (2, 6), and (3, 12). 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)

Please use full sentences and explain fully.

Answer 1

Part A

The graph passes through $(0,2),(2,6),(3,12)$.

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 $(2,6)$.

We obtain the slope to be

$m=\frac{6-2}{2-0}$

$\Rightarrow m=\frac{4}{2}=2$

Using $(0,2)$ and $(3,12)$.

We obtain the slope to be

$m=\frac{12-2}{3-0}$

$\Rightarrow m=\frac{10}{3}=3\frac{1}{3}$.

Since the slope is not constant(the same) everywhere, the function is non-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 $y=x^2$or $y=\sqrt{x}$ etc