Which line having the given slope and passing through the given point represents a direct variation?

,

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Verify each case

case A) For   point

The linear direct variation equation is equal to

For

substitute the value of x and the value of y in the equation and then compare the result

------> is true

therefore

This line represent a direct variation

case B) For   point

The linear direct variation equation is equal to

For

substitute the value of x and the value of y in the equation and then compare the result

------> is not true

therefore

This line not represent a direct variation

case C) For   point

The linear direct variation equation is equal to

For

substitute the value of x and the value of y in the equation and then compare the result

------> is not true

therefore

This line not represent a direct variation

case D) For   point

The linear direct variation equation is equal to

For

substitute the value of x and the value of y in the equation and then compare the result

------> is not true

therefore

This line not represent a direct variation

(1,4) is on graph of f(x)

f(1) = 4

so 1/4 f(x)

1/4 f(1)

1/4. ×4

1

so point for function 1/4. f(x) is (1,1)

answer: 100

step-by-step explanation: