Graphing Proportional Relationships Quick Check

Question

2 of 52 of 5 Items

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=36x
y equals 36 x

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

y=12x
y equals 12 x

y=2x

Answer 1

To derive the equation of the line through the origin based on the graph described, we can use the points plotted on the graph. The points provided are:

• (0, 0)
• (1, 12)
• (2, 24)
• (3, 36)

From the points, we can see that for every 1 foot (on the x-axis), the corresponding number of inches (on the y-axis) increases by 12 inches.

So, the ratio of inches to feet is:

\[ \frac{12 \text{ inches}}{1 \text{ foot}} = 12 \]

This indicates that the slope of the line (or the constant of proportionality) is 12. Therefore, the equation of the line can be expressed as:

\[ y = 12x \]

So the correct response is:

y = 12x