Part A
The graph passes through [tex](0,2),(2,6),(3,12)[/tex].
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 [tex](0,2)[/tex] and [tex](2,6)[/tex].
We obtain the slope to be
[tex]m=\frac{6-2}{2-0}[/tex]
[tex]\Rightarrow m=\frac{4}{2}=2[/tex]
Using [tex](0,2)[/tex] and [tex](3,12)[/tex].
We obtain the slope to be
[tex]m=\frac{12-2}{3-0}[/tex]
[tex]\Rightarrow m=\frac{10}{3}=3\frac{1}{3}[/tex].
Since the slope is not constant(the same) everywhere, the function is non-linear.
Part B
A linear function is of the form
[tex]y=mx+b[/tex]
where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
An example is [tex]y=2x-3[/tex]
A linear function can also be of the form,
[tex]ax+by=c[/tex] where [tex]a,b[/tex] and [tex]c[/tex] are constants.
An example is [tex]2x+4y=3[/tex]
A non linear function contains at least one of the following,
An example is [tex]xy=1[/tex] or [tex]y=x^2[/tex]or [tex]y=\sqrt{x}[/tex] etc
