Question

Of the following equations below, which equation represents a direct variation between x and y?
Select one:
A. 2y = 3x −7
B. y −4 = x +6
C. y +3 = x +3
D. 4y +1 = 4x−1

Answer 1

Answer:

C. y +3 = x +3

Step-by-step explanation:

We need to find in below option x has direct variation with y.

We solve for each;

A. $2y = 3x-7$

From above equation we can state that 2 times y is equal to 7 less than 3 times of x.

Hence it doesn't represent direct variation.  

B. $y-4 = x+6$

Solving above expression we get;

$y-4 = x+6\\y = x+6+4\\y=x+10$

From above equation we can state that y is equal to 10 more than x.

Hence it doesn't represent direct variation.

C. $y+3 = x+3$

Solving above expression we get;

$y+3 = x+3\\y = x+3-3\\y=x$

From above equation we can state that y is equal to x.

Hence it represent direct variation.

D. $4y+1 = 4x-1$

Solving above expression we get;

$4y+1 = 4x-1\\4y = 4x-1-1\\4y=4x-2$

From above equation we can state that 4 times y is equal to 2 less than 4 times of x.

Hence it doesn't represent direct variation.

Hence the Answer which represent direct variation of x and y is,

C. $y+3 = x+3$