Question

The propotional relationship between inches and feet is displayed on the graph. Derive the equation of the line through the origin
graph: 12, 24, 36,
y= 1/12x
y=2x
y=36x
y=12x

Answer 1

To derive the equation of the line that represents the proportional relationship between inches and feet, we first clarify the relationship between the two units of measurement.

1. **Understanding the Relationship**: There are 12 inches in a foot. This means that 1 foot corresponds to 12 inches. Therefore, if we define:
- \( x \) as the number of feet,
- \( y \) as the number of inches in feet,
we have the relation:

\[
y = 12x
\]

2. **Choosing the Correct Equation**: From the options provided:
- \( y = \frac{1}{12}x \)
- \( y = 2x \)
- \( y = 36x \)
- **\( y = 12x \)**

The correct equation that describes the relationship between inches and feet is:

\[
y = 12x
\]

In this equation, for each foot (1 unit of \( x \)), there are 12 inches (1 unit of \( y \)). Additionally, the line passes through the origin, which corresponds to 0 feet and 0 inches. The slope of the line is 12, indicating that for every increase of 1 foot, the measurement in inches increases by 12.

Thus, the answer is \( y = 12x \).