Question

A room is 15 feet tall. An architect wants to include a window that is 6 feet tall. The distance between the floor and the bottom of the window is b feet. The distance between the ceiling and the top of the window is a feet. This relationship can be described by the equation a=15-(b+6)Which variable is independent based on the the equation given ?What value of a would work with the given value for b?

Answer 1

Given:

Height of room, h = 15 ft

Height of window = 6 ft

Distance between the floor and bottom of the window = b ft

Distance between the ceiling and top of the window = a ft

The equation below represents this situation:

a = 15 - (b + 6)

• Which variable is independent based on the the equation given?

The independent variable is the variable that doesn't depend on other variables.

The inependent variable is also called the input variable.

Here, the independent variable is the distance between the floor and the bottom of the window.

Therefore, the independent variable is b

• What value of a would work with the given value for b?

Since we are not given any value for b, let's take a random value.

Take b = 3

To find the value of a, when b is 3, substitute 3 for b and evaluate.

We have:

`\begin{gathered} a=15-(3+6) \\ \\ a=15-9 \\ \\ a=6 \end{gathered}`

Therefore, when the distance between the floor and the bottom of the window is 3 feet, the distance between the ceiling and the top of the window is 6 feet.

ANSWER:

Independent variable = b