Question

The graphs below show measurements from cubes with different side lengths. Which pairs of variables have a linear relationship? Select two options.

Answer 1

The pairs of variables that have a linear relationship in the given graphs are the side length and volume, and the side length and surface area.

Step-by-step explanation:

The pairs of variables that have a linear relationship are:

1. Side length and volume
2. Side length and surface area

As the side length of a cube increases, its volume and surface area also increase. This relationship can be represented by a linear equation. For example, if the length of a cube's side is represented by x and its volume is represented by y, the equation would be y = kx, where k is a constant.

Answer 2

side length and perimeter of 1 face

area of 1 face and surface area

Step-by-step explanation:

The missing options are:

• side length and perimeter of 1 face

• perimeter of 1 face and area of 1 face

• surface area and volume

• area of 1 face and surface area

• side length and volume

In the picture attached, the cube measurements are shown:

In a linear relationship:

variable a / variable b = k

Case: side length and perimeter of 1 face

12/3 = 16/4 = 20/5 = 24/6 = 4

Case: perimeter of 1 face and area of 1 face

12/9 ≠ 16/16 ≠ 20/25 ≠ 24/36

Case: surface area and volume

54/27 ≠ 96/64 ≠ 150/125 ≠ 216/216

Case: area of 1 face and surface area

54/9 = 96/16 = 150/25 = 216/36 = 6

Case: side length and volume

27/3 ≠ 64/4 ≠ 125/5 ≠ 216/6