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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=2x
y equals 2 x

y=12x
y equals 12 x
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Answer 1

To derive the equation of the line through the origin based on the provided information, we can use the points given on the graph to identify the relationship between inches (y-axis) and feet (x-axis).

From the points provided:

• When \( x = 1 \), \( y = 12 \)
• When \( x = 2 \), \( y = 24 \)
• When \( x = 3 \), \( y = 36 \)

We can see that for every 1 foot (x increase of 1), the inches (y) increase by 12. Therefore, the ratio of inches to feet is 12 inches for every 1 foot.

This gives us the slope of the line as: \[ \text{slope} = \frac{y}{x} = 12 \]

Thus, the equation of the line can be expressed as: \[ y = 12x \]

So the correct response is: y = 12x