Question

Which pairs of variables have a linear relationship? Select

Answer 1

Answer:

Side length and perimeter of 1 face

Area of 1 face and surface area

Step-by-step explanation:

Suppose you are given cube with side length of x units.

Then

Side length = x units

Perimeter = 4x units

Area of 1 face $=x^2$ square units

Surface area $=6x^2$ square units

Volume $=x^3$ cubic units

A linear relationship is any equation that, when graphed, gives you a straight line.

Consider all options:

A. Side length and perimeter of 1 face is a linear relationship, because the graph of the function $y=kx$ is a straight line.

B. Perimeter of 1 face and area of 1 face is not a linear relationship, because the graph of this relationship is a quadratic parabola with equation $y=kx^2$.

C. Surface area and volume is not a linear relationship, because the graph of this relationship is a curve with equation $y=kx^{\frac{3}{2}}$.

D. Area of 1 face and surface area is a linear relationship, because the graph of the function $y=kx$ is a straight line.

E. Side length and volume is not a linear relationship, because the graph of this relationship is a cubic parabola with equation $y=kx^3$.

Answer 2

Answer:

Side length and perimeter of 1 face

Area of 1 face and surface area

Step-by-step explanation: