Question

the graphs below show measurements from cubes with different side lengths. which pairs of variables have a linear relationship? select two options. □ 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

Explanation:

1. Side length and perimeter of 1 face: A cube's face is a square. Perimeter of a square is \( P = 4s \) (where \( s \) is side length). This is a linear equation (\( y = 4x \)), so the relationship is linear.
2. Area of 1 face and surface area: A cube has 6 identical faces. Surface area \( SA = 6A \) (where \( A \) is area of one face). This is a linear equation (\( y = 6x \)), so the relationship is linear.

Other options:

• Perimeter of 1 face (\( 4s \)) and area of 1 face (\( s^2 \)): quadratic, not linear.
• Surface area (\( 6s^2 \)) and volume (\( s^3 \)): non - linear.
• Side length (\( s \)) and volume (\( s^3 \)): cubic, not linear.

Answer:

• side length and perimeter of 1 face
• area of 1 face and surface area