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=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
y=12x
To derive the equation of the line through the origin, we can use the ratio between inches and feet.
Looking at the graph, we can see that for every 1 foot increase on the x-axis, there is a 12 inch increase on the y-axis.
Therefore, the equation of the line through the origin is:
y = 12x
To derive the equation of the line through the origin, we need to determine the slope of the line.
In this case, the line passes through the origin, which means it intersects the y-axis at (0,0). Since the line is upward-sloping, the slope is determined by the change in y divided by the change in x between any two points on the line.
Looking at the given graph, we can see that for each increase of 1 foot (1 unit on the x-axis), the line rises by 12 inches (12 units on the y-axis). This means the slope of the line is 12/1 or simply 12.
Therefore, the equation of the line through the origin can be written as y = 12x. This represents the proportional relationship between inches (y) and feet (x), where for every unit increase in x, there is a corresponding increase of 12 units in y.