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\\4 & 5\\8 & 7\\12 & 9\\16 & 11\end{array}\right][/tex]
All these points have been plotted below, so you can realize 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-5=\frac{7-5}{8-4}(x-4) \\ \\ y-5=\frac{2}{4}(x-4) \\ \\ y=\frac{1}{2}x+5-2 \\ \\ y=\frac{1}{2}x+3 \\ \\ \\ Where: \\ \\ (x_{1},y_{1})=(4,5) \\ \\ (x_{2},y_{2})=(8,7)[/tex]
Finally, the equation is:
[tex]\boxed{y=\frac{1}{2}x+3}[/tex]
