Write a function rule for "the output is six times the input".

y=6x

Step-by-step explanation:

In this function, the input is the variable x. The problem says that the output is six times the input, so we will need to multiply the input by 6. To write this as a function, set the output (y) equal to 6 times the input (x):

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: