Check that 2b+b and 3b have the same value when b is 1,2, and 3. Do 2b+b and 3b have the same value for all values of b? Explain your reasoning

Expression 2b+b and 3b have same values for all values of b.

Step-by-step explanation:

Given the two expression and and values of b as 1, 2 and 3.

Consider first expression that is, .

Substituting the value of ,

....1

Substituting the value of ,

....2

Substituting the value of ,

....3

Consider second expression that is, .

Substituting the value of ,

....4

Substituting the value of ,

....5

Substituting the value of ,

....6

For value of b=1, equation 1 and equation 4 are same, for value of b=2, equation 2 and equation 5 are same and for value of b=3 equation 3 and equation 6 are same.

Therefore both expression are same for all values of b.

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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: