Suppose y varies directly as x , and y=−319 when x = 29. based on this information, write a direct variation equation that relates x and y .

Step-by-step explanation:

If y varies directly as x, then we can write the relation

where k is the constant of proportionality.

We substitute y=-319 when x=29.

This implies that:

The variation equation now becomes

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: