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=12x
y equals 12 x
y=112x
y equals Start Fraction 1 over 12 End Fraction x
y=2x
y equals 2 x
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page 15 of 15
To derive the equation of the line through the origin, we need to determine the slope of the line. The slope of a line can be calculated using the formula (change in y)/(change in x).
Using the given points on the line: (0,0) and (3,36), we can calculate the slope:
(change in y) = 36 - 0 = 36
(change in x) = 3 - 0 = 3
Slope = (36)/(3) = 12
Since the line passes through the origin (0,0), the equation of the line can be written as:
y = 12x
Therefore, the correct answer is:
y=12x
y equals 12 x