Graphing Proportional Relationships Quick Check
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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=12x
y equals 12 x
y=112x
y equals Start Fraction 1 over 12 End Fraction x
y=36x
y equals 36 x
y=2x
y equals 2 x
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The correct equation of the line through the origin is y = 12x.
r u sure
I apologize for the confusion. The correct equation of the line through the origin is y = 12x.
To derive the equation of the line through the origin, we need to find the slope of the line. The slope of a line is given by the formula:
slope = (change in y) / (change in x)
Looking at the graph, we can see that for every 1 unit increase in x (feet), there is a 12 unit increase in y (inches).
Therefore, the slope of the line is 12.
Since the line passes through the origin, the equation of the line can now be written as:
y = mx
where m is the slope.
Substituting the value of the slope, the equation becomes:
y = 12x
So the correct answer is:
y = 12x