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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=36x
y equals 36 x

y=12x
y equals 12 x

y=2x
y equals 2 x
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Answer 1

In the graph described, the points plotted indicate a linear relationship between inches and feet, specifically:

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

Since the line goes through the origin (0,0), we are looking for an equation in the form of \( y = mx \), where \( m \) is the slope.

To find the slope \( m \), we can use the point (1, 12):

\[ m = \frac{\text{change in } y}{\text{change in } x} = \frac{12 - 0}{1 - 0} = 12 \]

So, the equation of the line is:

\[ y = 12x \]

Thus, the correct response is:

y = 12x