Answer: The correct option is
(C) [tex]12y=8x+3.[/tex]
Step-by-step explanation: We are given to select the correct equation that is equivalent to the following equation :
[tex]y=\dfrac{2}{3}x+\dfrac{1}{4}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To check the equivalent expression, we need to simplify equation (i).
The simplification of equation (i) is as follows :
[tex]y=\dfrac{2}{3}x+\dfrac{1}{4}\\\\\\\Rightarrow y=\dfrac{2\times4x+1\times3}{12}\\\\\\\Rightarrow y=\dfrac{8x+3}{12}\\\\\Rightarrow 12y=8x+3.[/tex]
Thus, the required equivalent equation is [tex]12y=8x+3.[/tex]
Option (C) is CORRECT.
