1. Find the equation and solve for k: y varies inversely as x and y = 6 when x = 18.​

An inverse function is y = k/x

replace x and y with the given values:

6 = k/18

Solve for k by multiplying both sides by 18:

k = 108

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

answer: 8

step-by-step explanation: