In class, matthew stated "i think that a negative is like an opposite. that is why multiplying a negative times a negative equals a positive. the opposite of negative is positive, so it is just like multiplying the opposite of a negative twice, which is two positives." do you agree or disagree with this statement? what would you say in response to him?

I agree and I would say that he is pretty much right because like he said whenever you multiply negative by positive, you get negative and -9 and positive 9 are both 9 steps away from zero on the line, meaning they are opposites.

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:

step-by-step explanation: