Answer :
For this problem, we were informed that a certain variable "y" is directly proportional to the variable "x" and that when "x" is equal to 41, "y" is equal to -3.
When two variables are directly proportional we can write their relation as shown below:
[tex]y=kx[/tex]Where "k" is a constant number. We can use the datapoint given to us (41, -3) to determine k. This is shown below:
[tex]\begin{gathered} -3=k\cdot41 \\ k=\frac{-3}{41} \end{gathered}[/tex]With this value, we can write the full expression, as shown below:
[tex]y=\frac{-3}{41}x[/tex]We need to determine the value of "y" when "x" is equal to 46, therefore we have:
[tex]\begin{gathered} y=\frac{-3}{41}\cdot46 \\ y=-3.37 \end{gathered}[/tex]The value of y is approximately -3.37