Answer:
The equation will be: Â [tex]y=4x[/tex]
Step-by-step explanation:
Side lengths[tex](x)[/tex] ⇒   4.5    8.5     10.25    13.75
Perimeter [tex](y)[/tex]   ⇒   18     34       41       55
First we will pick any two ordered pairs in form of point like [tex](x,y)[/tex]. So, here [tex](x_{1}, y_{1})= (4.5, 18)[/tex] and [tex](x_{2}, y_{2})= (8.5, 34)[/tex]
Now, the slope will be: Â [tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}= \frac{34-18}{8.5-4.5}=\frac{16}{4}=4[/tex]
So, the equation using the point-slope form will be..............
[tex]y-y_{1}=m(x-x_{1})\\ \\ y-18=4(x-4.5)\\ \\ y-18=4x-18\\ \\ y=4x[/tex]
Thus, the equation that represents the relationship between the side length[tex](x)[/tex] and the perimeter[tex](y)[/tex] will be: Â [tex]y=4x[/tex]
