Question

If y is directly proportional to x and y=−3 when x=41, find y if x=46. (Round off your answer to the nearest hundredth.)

Answer 1

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:

`y=kx`

Where "k" is a constant number. We can use the datapoint given to us (41, -3) to determine k. This is shown below:

`\begin{gathered} -3=k\cdot41 \\ k=(-3)/(41) \end{gathered}`

With this value, we can write the full expression, as shown below:

`y=(-3)/(41)x`

We need to determine the value of "y" when "x" is equal to 46, therefore we have:

`\begin{gathered} y=(-3)/(41)\cdot46 \\ y=-3.37 \end{gathered}`

The value of y is approximately -3.37