The tables below show the values of f (x) and g (x) for different values of x:

f (x) = 2(3)×

x f(x)
-2 0.22
-1 0.67
0 2
1 6
2 18

g(x)=3×+1

x g(x)
-2 1.11
-1 1.33
0 2
1 4
2 10

based on the tables what is the solution to the equation 2(3)×=3×+1?

a) x=-1
b) x=0
c) x=1
d) x=2

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: