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Question

The graph of a proportional relationship passes through the point (4,10). Explain how to find the constant of proportionality. (Remember that the graph of a proportional relationship passes through the origin)

Answer 1

Let x and y be two proportional quantities.

Then the constant of proportionality k is defined as:

 

y/x = k

 

Therefore, 

 

y = kx

 

This is represented by a straight line graph through the origin. The slope of that graph is the constant of proportionality. 

 

The slope k is found by dividing the change in y between two points over the change in x over those same two points. This is the slope of the line.

 

Since we know this line passes through (4,10) and the origin (0,0) then 

 

k = (10-0)/4-0) = 10/4 = 2.5