The relationships which have the same constant of proportionality between y and x as in the equation y = 1/3x are C and E.
What is the slope of a line?
The slope of a line is the ratio that determines the steepness as well as the direction of the line.
How to find the slope of a line?
Let the two points on a line be [tex](x_{1} , y_{1} )[/tex] and [tex](x_{2} , y_{2 )[/tex]. The slope can be found as follows:
[tex]\frac{(y_{2} -y_{1} )}{(x_{2} -x_{1} )}[/tex]
The constant of proportionality in the given problem can be understood as the slope of the line. Thus the lines with their slopes as 1/3 will have the same constant of proportionality as the equation y = 1/3 x.
We can observe the graphs given and find their respective slopes. It can be done as follows:
(3 - 0)/(0 + 3) = 1
(3 - 0)/(1 - 0) = 3
(1 - 0)/(3 - 0) = 1/3
(29.1 - 4.8)/(9.7 - 1..6) = 3.111
(0.8 - 0.5)/(2.4 - 1.5) = 1/3
Therefore, graphs C and E have relationships that have the same constant of proportionality between y and x as in the equation y = 1/3 x.
Learn more about slopes here-https://brainly.com/question/3493733
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