Question

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

Answer 1

Answer:

$m=2/3$, $(9,6)$

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 $y/x=k$ or $y=kx$

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 $m=2/3$   point $(9,6)$

The linear direct variation equation is equal to

$y=(2/3)x$

For $x=9, y=6$

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

$6=(2/3)(9)$

$6=6$ ------> is true

therefore

This line represent a direct variation

case B) For $m=2/3$   point $(6,9)$

The linear direct variation equation is equal to

$y=(2/3)x$

For $x=6, y=9$

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

$9=(2/3)(6)$

$9=4$ ------> is not true

therefore

This line not represent a direct variation

case C) For $m=2/3$   point $(9,-6)$

The linear direct variation equation is equal to

$y=(2/3)x$

For $x=9, y=-6$

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

$-6=(2/3)(9)$

$-6=6$ ------> is not true

therefore

This line not represent a direct variation

case D) For $m=-2/3$   point $(9,6)$

The linear direct variation equation is equal to

$y=-(2/3)x$

For $x=9, y=6$

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

$6=-(2/3)(9)$

$6=-6$ ------> is not true

therefore

This line not represent a direct variation