In a certain function, y varies directly with x. If y = 6 when x = 8, find x when y = 9.

If y = 6 when x = 8, then value of "x" when y = 9 is equal to 12Solution:Given that , In a certain function, y varies directly with xAnd x = 8 when y = 6,We have to find what will be the value of x when y = 9Now, from the given information,[tex]\begin{array}{l}{y \alpha x} \\\\ {y=c x \rightarrow(1)}\end{array}[/tex]where c is the proportionality constant[tex]\begin{array}{l}{\text { Now, substitute } x=8 \text { and } y=6 \text { in }(1)} \\\\ {\rightarrow 8=c(6) \rightarrow c=\frac{8}{6}} \\\\ {\rightarrow c=\frac{4}{3}} \\\\ {\text { Then, }(1) \rightarrow x=\frac{4}{3} y} \\\\ {\text { So, when } y=9} \\\\ {\rightarrow x=\frac{4}{3}(9)} \\\\ {\rightarrow x=4 \times 3} \\\\ {\rightarrow x=12}\end{array}[/tex]Hence, x value is 12 when y value is 9