Question

If y varies directly as x, and y is 12 when x is 1.2, what is the constant of variation for this relation? A) 1 B) 10 C) 10.8 D) 14.4

Answer 1

$\bf \begin{array}{cccccclllll}&\\ \textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\&\\ \textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\&\\ y&=&{{ k}}&\cdot&x&\\ &\\ && y={{ k }}x&\\ \end{array}& \\\\\\ \textit{we know that } \begin{cases} y=12\\ x=1.2 \end{cases}\implies y=kx\implies 12=k\cdot 1.2$

solve for "k" to find "k", or the "constant of variation"

Answer 2

Direct variation is expressed as y = kx, where k is the constant of variation.

You are given that y = 12 and x = 1.2, so you can find k by substituting this into the direct variation equation:
y = kx
(12) = k(1.2)
k = 10