Answer:
This relation is a function because a function [tex]f[/tex] from a set [tex]A[/tex] to a set [tex]B[/tex] is a relation that assigns to each element [tex]x[/tex] in the set [tex]A[/tex] exactly one element [tex]y[/tex] in the set [tex]B[/tex]. The set [tex]A[/tex] is the domain (also called the set of inputs) of the function and the set [tex]B[/tex] contains the range (also called the set of outputs). So we have that:
[tex]\left[\begin{array}{cc}x & y\\1 & 0\\2 & 4\\3 & 8\\4 & 12\end{array}\right][/tex]
We have plotted all the points below. As you can see, this is a linear function. Therefore, with two points we can get the equation, so:
[tex]The \ equation \ of \ the \ line \ with \ slope \ m \\ passing \ through \ the \ point \ (x_{1},y_{1}) \ is:\\ \\ y-y_{1}=m(x-x_{1}) \\ \\ \\ y-0=\frac{4-0}{2-1}(x-1) \\ \\ y=4(x-1) \\ \\ y=4x-4 \\ \\ \\ Where: \\ \\ (x_{1},y_{1})=(1,0) \\ \\ (x_{2},y_{2})=(2,4)[/tex]
Finally, the equation is:
[tex]\boxed{y=4x-4}[/tex]
