Use the image to answer the question.

Question

Use the image to answer the 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

Bot GPT 4-o mini answered
10 days ago

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