What are the answers?

See below.

Step-by-step explanation:

The left side of the equations simplifies to 4x + 4.

For No solution we could write 4x + 5  ( because 4x + 4 cannot be = 4x +5 for any value of x).)

For one solution we could have 3x + 10. (solving gives x = 6 one solution)

For infinitely many : 4x + 4. (the left and right sides are identical so there are infinite solutions)

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: