[tex]\frac{y}{x} = k[/tex]
[tex]\frac{6}{72} = k[/tex]
[tex]\frac{1}{12} = k[/tex]
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[tex]\frac{y}{x} = k[/tex]
[tex]\frac{y}{8} = \frac{1}{12}[/tex]
12y = 8
[tex]y = \frac{8}{12}[/tex]
[tex]y = \frac{2}{3}[/tex]
y = [tex]\frac{2}{3}[/tex]
given y ∝ x
To convert to an equation multiply by k the constant of variation
y = kx
to find k use the given condition y = 6 when x = 72
y = kx ⇒ k = [tex]\frac{y}{x}[/tex] = [tex]\frac{6}{72}[/tex] = [tex]\frac{1}{12}[/tex]
equation is → y = [tex]\frac{1}{12}[/tex] x
when x = 8 then
y = [tex]\frac{1}{12}[/tex] × 8 = [tex]\frac{8}{12}[/tex] = [tex]\frac{2}{3}[/tex]
