What equation represents the proportional relationship displayed in the table?

x 0 4 7 8
y 0 24 42 48
enter your answer in the box to complete the equation.

y =
x

Step-by-step explanation:

Given:

The table is given as:

x   0    4       7       8

y   0    24    42     48

The relationship between 'x' and 'y' is a proportional relationship.

A proportional relationship is one in which one variable varies directly with the other by a factor of 'k' also known as constant of proportionality and

A proportional relationship is given as:

Now, we plug in 'x' and 'y' values and find the value of 'k'.

Let

Therefore, the constant of proportionality is 6. Hence the complete equation is given as:

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:

square root

step-by-step explanation: