the graphs below show measurements from cubes with different side lengths. which pairs of variables have a…

Answer:

1. side length and perimeter of 1 face
2. area of 1 face and surface area

Explanation:

Step1: Recall relevant formulas

Let the side - length of a cube be $s$. The perimeter of 1 face $P = 4s$, which is a linear function ($y = mx$ form where $m = 4$ and $y=P$, $x = s$). The area of 1 face $A_1=s^{2}$, the surface - area of a cube $A = 6s^{2}$. If we let $x = A_1$ and $y = A$, then $y = 6x$, which is a linear function. The perimeter of 1 face $P = 4s$ and the area of 1 face $A_1=s^{2}$, $A_1=\frac{P^{2}}{16}$ (since $s=\frac{P}{4}$), which is a quadratic relationship. The surface - area $A = 6s^{2}$ and the volume $V=s^{3}$, which is not a linear relationship. The side - length $s$ and the volume $V=s^{3}$, which is a cubic relationship.