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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=2x
y equals 2 x

y=12x
y equals 12 x

y=36x
y equals 36 x
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Answer 1

To derive the equation of the line representing the relationship between inches and feet from the graph, we need to determine the slope based on the points provided.

From the graph:

• The points given are (0, 0), (1, 12), (2, 24), and (3, 36).
• The relationship is linear, and we can find the slope (m) using the formula:

\[ m = \frac{\text{change in } y}{\text{change in } x} \]

Using the points (1, 12) and (0, 0):

\[ m = \frac{12 - 0}{1 - 0} = \frac{12}{1} = 12 \]

The y-intercept (b) is 0 since the line passes through the origin (0, 0).

Thus, the equation of the line is:

\[ y = 12x \]

So the answer is:

y = 12x