Which equation represents a proportional relationship?
a. y=−5(x+1)y=−5(x+1)
b. y5=x+1y5=x+1
c. y=−xy=−x
d. xy=15

Proportional relationships compare two equal ratios. when thinking of proportions, you want to be concerned with multiplication, and you want to ask yourself if the equation would leave you multiplying or dividing by the same ratio for each and every x and y value. it sounds a little confusing, but it's easier in practice.

choice A is incorrect, because it throws addition into the mix. with addition there, there isn't a set, constant ratio that applies to all of your outputs.
choice B is incorrect for the same reason. rather than multiplying by the same ratio for every input to get an output, you're throwing addition in.
choice C is the correct answer. you multiply every x value by -1 to get your output.
choice D is incorrect, because you aren't dividing by the same ratio every time. get y alone:
xy = 15
y = (15/x)
the x value changes, so for the first input, you might choose 1. for the second, you might choose 43. this means that you aren't multiplying by the same ratio, because the value is changing.

The 8th term is 512