Final answer:
The equation y = 15x represents a proportional relationship because it follows the form y = kx with k being a constant, in this case, 15, and there is no y-intercept.
Step-by-step explanation:
The equation that represents a proportional relationship is one where the ratio of the dependent variable to the independent variable is constant. A proportional relationship in linear equations is of the form y = kx, where k is the proportionality constant and there is no y-intercept or the y-intercept is zero.
Looking at the given options:
y = −5(x + 1) is not proportional because it includes an extra term that will change depending on the value of x.
y = 15x is proportional because it follows the direct proportionality form with a constant k of 15.
y = −x is proportional, but since there is another option that is also proportional, we look for the one with a positive constant k.
y = 5x + 1 is not proportional because it includes a y-intercept of 1, which violates the conditions of a direct proportional relationship.
Therefore, the equation y = 15x represents a proportional relationship.