Lydia writes the equation below with a missing value.
y = 5 x minus box
She puts a value in the box and says that the equation represents a direct variation. Which explains whether the equation could represent a direct variation?
If she puts 0 in the box she would have a direct variation.
If she puts 5 in the box she would have a direct variation.
The equation is not of the form y = k x, so it cannot represent a direct variation.
The equation has a minus sign, so it cannot represent a direct variation.
The correct answer is:
If she puts 0 in the box she would have a direct variation.
A direct variation is represented by an equation of the form y = kx, where k is a constant. In this case, if Lydia puts 0 in the box, the equation becomes y = 5x - 0, which simplifies to y = 5x. This is indeed a direct variation equation, where k = 5. Therefore, if she puts 0 in the box, the equation represents a direct variation.
The correct answer is: The equation is not of the form y = k x, so it cannot represent a direct variation.
In direct variation, the equation is of the form y = kx, where k is a constant. Since the equation given is not in this form, it cannot represent a direct variation.