Question

Which equation(s) represent(s) proportional relationship(s) with a constant of proportionality equal to −2?

Select ALL that apply.

Responses

y=2x
y = 2 x

y =−2x
y = − 2 x

2y=−2x+2
2 y = − 2 x + 2

2y=−4x
2 y = − 4 x

y=x−2
y = x − 2

y+2=2x+2

Answer 1

The equations representing proportional relationships with a constant of proportionality equal to -2 are y = -2x and 2y = -4x, once the latter is simplified.

Step-by-step explanation:

A proportional relationship is one in which two quantities vary directly with each other. This means if you have an equation y = kx, where k is a constant, y and x have a proportional relationship, with k being the constant of proportionality. Looking at the equations provided, your goal is to identify which equations represent a proportional relationship where the constant of proportionality is −2.

y = 2x : This equation does not represent a proportional relationship with a constant of −2; the constant here is 2.

y = −2x : This is a direct proportional relationship with a constant of −2, as required.

2y = −2x + 2 : This equation includes an additional constant term, +2, which means it is not a proportional relationship, as it does not have the form y = kx.

2y = −4x : Once this equation is simplified (dividing both sides by 2), it becomes y = −2x, indicating a proportional relationship with a constant of −2.

y = x − 2 : Like the third equation, this one contains an additional term, − 2, which prevents it from being a proportional relationship with a constant of −2.

y + 2 = 2x + 2 : This equation cannot be simplified to the form y = kx without an extra constant, thus it also does not represent a proportional relationship.

Based on this analysis, the equations that represent proportional relationships with a constant of proportionality equal to −2 are y = −2x and 2y = −4x.