Answer:
[tex]k=\frac{2}{3}[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In this problem we have
[tex]3y=2x[/tex]
Isolate the variable y
Divide by 3 both sides
[tex]y=\frac{2}{3}x[/tex]
Remember that
In a proportional relationship the constant of proportionality k is equal to the slope m of the line
The slope of the line m is
[tex]m=\frac{2}{3}[/tex]
therefore
The constant of proportionality k is
[tex]k=\frac{2}{3}[/tex]
The constant of proportionality is [tex]k=\dfrac{2}{3}[/tex]
A relation between two variables, [tex]x[/tex] and [tex]y[/tex], represent a proportional variation if it can be expressed in the form [tex]y=kx[/tex]
We have given that
[tex]3y=2x[/tex]
Solve for y,
[tex]y=\dfrac{2}{3}x[/tex]
Remember that the constant of proportionality [tex]k[/tex] is equal to the gradient [tex]m[/tex] of the line.
Therefore, the gradient of the line [tex]m[/tex] is
[tex]m=\dfrac{2}{3}[/tex]
Therefore , the constant of proportionality [tex]k[/tex] is
[tex]k=\dfrac{2}{3}[/tex]
Learn more about constant of proportionality
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