Question

An illustration shows a graph labeled Inches per Feet. The horizontal axis is labeled feet and ranges from 0 to 4 in increments of 1. The vertical axis is labeled Inches and ranges from 0 to 40 in increments of 4. An upward slanting line segment connects points plotted at left parenthesis 0 comma 0 right parenthesis, left parenthesis 1 comma 12 right parenthesis, left parenthesis 2 comma 24 right parenthesis, and left parenthesis 3 comma 36 right parenthesis.
The proportional relationship between inches and feet is displayed on the graph. Derive the equation of the line through the origin.

(1 point)
Responses

y=112x
y equals Start Fraction 1 over 12 End Fraction x

y=12x
y equals 12 x

y=36x
y equals 36 x

y=2x

Answer 1

To derive the equation of the line represented in the graph, we need to identify the relationship between the input (feet) and output (inches).

From the points given:

- At 0 feet, 0 inches: \( (0, 0) \)
- At 1 foot, 12 inches: \( (1, 12) \)
- At 2 feet, 24 inches: \( (2, 24) \)
- At 3 feet, 36 inches: \( (3, 36) \)

We can observe that for every 1 foot increase, there is a corresponding increase of 12 inches. Therefore, the relationship can be described by the slope of the line, which is:

\[
\text{slope} = \frac{\text{change in inches}}{\text{change in feet}} = \frac{12 - 0}{1 - 0} = 12
\]

Since the line passes through the origin (0,0), this confirms that the equation of the line in slope-intercept form \( y = mx + b \) results in:

\[
y = 12x
\]

Thus, the correct equation is:

**y = 12x**