The constant of proportionality of the equation is: C) [tex]\frac{9}{2}[/tex]
Given:
[tex]\frac{x}{y} =\frac{2}{9}[/tex]
Recall:
Constant of proportionality which is denoted by [tex]k[/tex] is usually expressed as:
[tex]k = \frac{y}{x}[/tex]
To find the constant of proportionality of the equation, rewrite the equation such that [tex]k = \frac{y}{x}[/tex]
[tex]\frac{x}{y} =\frac{2}{9}\\[/tex]
Cross multiply:
[tex]2\times y = 9\times x\\2y = 9x\\\frac{2y}{2}= \frac{9x}{2} \\y =\frac{9x}{2}\\\frac{y}{x} = \frac{9}{2}[/tex]
[tex]k =\frac{9}{2}[/tex]
Therefore, the constant of proportionality is: C) [tex]\frac{9}{2}[/tex]
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