INVERSE VARIATION
[tex] \\ \\ [/tex]
If y varies inversely as x and y= 15 when x= 3, find the value y when x= 5.
[tex] \\ y = \frac{k}{x} \\ \\ [/tex]
Evaluate the values
[tex] \\ 15 = \frac{k}{3} \\ \\ [/tex]
Multiply 3 to both sides
[tex] \\ (3)(15) = \frac{k}{3} (3) \\ \\ [/tex]
Cancel both 3 from the right side
[tex] \\ (3)(15) = \frac{k}{ \cancel3} ( \cancel3) \\ \\ [/tex]
Multiply 3 by 15
[tex] \\ \boxed{k = 45} \\ \\ [/tex]
Find y when x= 5 and use the k value from the first problem.
[tex] \\ y = \frac{k}{x} \\ \\ [/tex]
Evaluate the values
[tex] \\ y = \frac{45}{5} \\ \\ [/tex]
Divide
[tex] \\ \large \green{ \boxed{ \green{ \sf{y = 9}}}} \\ \\ \\ \\ [/tex]
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