TELL WHETHER THE EQUATION REPRESENTS DIRECT VARIATION

Mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other.

y = kx

here k is constant of variation.

Problem 1 :

y = - 8x

Solution :

This equation represents a direct variation, because it is in the form y = kx. The constant of variation is -8.

Problem 2 :

y - 4 = 3x

Solution :

Solve the equation for y.

y = 3x + 4

This equation does not represents a direct variation, because it is not in the form y = kx.

Problem 3 :

3y - 7 = 10x

Solution :

3y - 7 = 10x

Solve the equation for y.

3y = 10x + 7

y = (10/3) x + (7/3)

This equation does not represents a direct variation, because it is not in the form y = kx.

Problem 4 :

2y - 5x = 0

Solution :

2y - 5x = 0

Solve the equation for y.

2y = 5x

y = (5/2) x

This equation represents a direct variation, because it is in the form y = kx. The constant of variation is 5/2.

Problem 5 :

5y = -4x

Solution :

5y = -4x

Solve the equation for y.

y = (-4/5) x

This equation represents a direct variation, because it is in the form y = kx. The constant of variation is -4/5.

Problem 6 :

6y = x

Solution :

6y = x

Solve the equation for y.

y = (1/6) x

This equation represents a direct variation, because it is in the form y = kx. The constant of variation is 1/6.

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