Question

Instructions: If varies directly as and =−16 when =4, find when =9. Write the equation using the given information, then use the equation to solve for . Use the forward slash (i.e. "/") for all fractions (e.g. -1/2 is the same as −12).

Answer 1

If y varies directly with x, with a constant of proportionality k, then the equation that relates x and y is:

$y=kx$

To solve the problem, use the first pair of data x=4, y=-16 to find the value of the constant of proportionality k. Next, use the value of k to write down the equation that relates x and y for this case, and use it to find the value of y when x=9.

Replace y=-16 and x=4 into the equation and solve for k:

$\begin{gathered} y=kx \\ \Rightarrow-16=k(4) \\ \Rightarrow-16=4k \\ \Rightarrow\frac{-16}{4}=k \\ \Rightarrow-4=k \\ \\ \therefore\quad\,k=-4 \end{gathered}$

Since the value of k is -4, then the equation that relates x and y is:

$y=-4x$

Replace x=9 to find the value of y when x=9.

$y=-4(9)=-36$

Therefore, the answers are:

Equation: y=-4x

Solution: y=-36