the value of y varies directly with x, and when x = 1/4 , y = 25. What is the value of y when x is 2 1/3 need help ASAP

Accepted Solution

Answer:[tex]y=233\frac{1}{3}[/tex]Step-by-step explanation:we know thatA relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]In this problem we haveFor [tex]x=1/4, y=25[/tex]Find the value of k (constant of proportionality)[tex]y/x=k[/tex] -----> [tex]k=25/(1/4)=100[/tex]The linear equation is [tex]y=100x[/tex]Find the value of y when the value of [tex]x=2\frac{1}{3}[/tex]substitute the value of x in the equation but first convert to an improper fraction[tex]x=2\frac{1}{3}=\frac{2*3+1}{3}=\frac{7}{3}[/tex][tex]y=100(\frac{7}{3})=\frac{700}{3}[/tex]convert the result in mixed number[tex]\frac{700}{3}=\frac{699}{3}+\frac{1}{3}=233\frac{1}{3}[/tex]