Question

1. what relationship exists between two variables when their ratio is a constant?

a negative slope
an inverse proportion
a direct proportion

Explanation:

When two variables have a constant ratio, it means \( y = kx \) (where \( k=\frac{y}{x}\) is the constant). This is the equation of a direct proportion. A negative slope would imply \( y = -mx + b\) (linear but not a constant ratio unless \(b = 0\) and \(m\) is negative, but even then it's not about ratio being constant). An inverse proportion is \( y=\frac{k}{x}\) (ratio \( \frac{y}{x}=\frac{k}{x^{2}}\) which is not constant).

Answer:

a direct proportion