Question

Which explains whether or not the function represents a direct variation?

Answer 1

Answer:

The function represents a direct variation

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a linear direct variation the line passes through the origin and the constant of proportionality k is equal to the slope m

Let

$A(0,0)$ ------> the line passes through the origin

$B(2,10)$

Find the value of k------> substitute the value of x and y

$y/x=k$-----> $k=10/2=5$

$C(4,20)$

Find the value of k------> substitute the value of x and y

$y/x=k$-----> $k=20/4=5$

$D(6,30)$

Find the value of k------> substitute the value of x and y

$y/x=k$-----> $k=30/6=5$

$E(8,40)$

Find the value of k------> substitute the value of x and y

$y/x=k$-----> $k=40/8=5$

The value of k is equal in all the points of the table and the line passes through the origin

therefore

The function represents a direct variation

the equation of the direct variation is equal to

$f(x)=5x$

Answer 2

Direct variation is when x increases, y increases, when x decreases, y decresaes

notice that the time (x) increases
if the cost collumn (y) incresaes as well, then it is direct

it does go up

it is direct because x and y both increase and decrease together