The two linear functions ƒ(x) and g(x) are shown below.

ƒ(x) = x + 3
Which of the following is true?

The rate of change of the function g(x) is –2.
The rate of change of ƒ(x) is times the rate of change of g(x).
The rate of change of ƒ(x) is greater than the rate of change of g(x).
The product of the rate of changes of ƒ(x) and g(x) is -6.

Step-by-step explanation:

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:

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)