Question

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.

Answer 1

Correct answer: "If she puts 0 in the box she would have a direct variation."

Reason: A direct variation has the form y = kx (no constant term), so the y-intercept must be 0. Putting 0 in the box gives y = 5x, which is a direct variation. Putting 5 would give y = 5x − 5 (not a direct variation). The presence of a minus sign alone doesn't rule it out — only a nonzero constant term does.