Respuesta :
The constant of proportionality [tex]k[/tex] is [tex]\frac{1}{5}[/tex].
What is constant of proportionality.
The constant of proportionality is the constant value of the ratio between two proportional quantities.
[tex]$k=\frac{y}{x}$[/tex]
Where [tex]k[/tex] is the constant of proportionality.
It is given that the table which shows the relationship [tex]y=kx[/tex] is,
x y
60 12
45 9
30 6
15 3
We have to find the value of [tex]k[/tex].
According to the formula of constant of proportionality,
Let,
[tex]${{k}_{1}}=\frac{{{y}_{1}}}{{{x}_{1}}}$[/tex]
[tex]${{k}_{1}}=\frac{12}{60}[/tex]
[tex]$\therefore {{k}_{1}}=\frac{1}{5}$[/tex]
Now,
Let,
[tex]${{k}_{2}}=\frac{{{y}_{2}}}{{{x}_{2}}}$[/tex]
[tex]${{k}_{2}}=\frac{9}{45}[/tex]
[tex]$\therefore {{k}_{2}}=\frac{1}{5}$[/tex]
The third is,
[tex]${{k}_{3}}=\frac{6}{30}[/tex]
[tex]$\therefore {{k}_{3}}=\frac{1}{5}$[/tex]
and
[tex]${{k}_{4}}=\frac{3}{15}[/tex]
[tex]$\therefore {{k}_{4}}=\frac{1}{5}$[/tex]
Hence, the Option [tex]$C$[/tex] is correct answer.
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