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.

Question

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=2x
y equals 2 x

y=36x
y equals 36 x

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

y=12x

Answer 1

To determine the equation of the line shown in the graph, we need to analyze the plotted points and the relationship between inches and feet.

From the points provided on the graph:

• At 0 feet, there are 0 inches.
• At 1 foot, there are 12 inches.
• At 2 feet, there are 24 inches.
• At 3 feet, there are 36 inches.

We can see that for every 1 foot increase, the number of inches increases by 12.

This indicates a proportional relationship, which can be expressed as \( y = mx \), where \( m \) is the constant of proportionality (the slope). In this case, the slope \( m \) is 12, since for every foot \( x \), the inches \( y \) is given by \( y = 12x \).

Therefore, the correct equation of the line through the origin is:

\[ y = 12x \]

So the correct response is: y = 12x