Question

Write the equation expressing the relationship "y varies directly as x." use k as the constant of proportionality.

Answer 1

The equation expressing the statement "y varies directly as x"  is $y=kx.$

Explanation

The statement that $y$ varies directly as $x$ is analogous to saying that  the ratio of $y$ to $x$ is constant. In other words, when $x$ increases, $y$ likewise increases and that when $x$ decreases, $y$ decreases proportionally.

Mathematically, we express the relationship that the ration of $y$ is to $x$ is constant is expressed as; $\frac{y}{x} =k$ where $k$ is the constant of proportionality.

We can then solve the relationship for $y$ to determine the correct form of the relationship as shown below,

$\frac{y}{x} =k\\\rightarrow y=kx$

Answer 2

The equation expressing the relationship "y varies directly as x" using k as the constant of proportionality is y = kx  hope this helps