Answer
$d$ varies directly as $t$.
The constant of variation is $58$.
The function rule is $d = 58t$.
Work Step by Step
To find the rule, we plug the $x$ values and $y$ values into the ratio $\frac{y}{x} = k$ to see if each set of $x$ and $y$ have the same constant of variation ($k$). If they do, then $y$ varies directly with $x$.
In these sets of inputs, $x$ is the time $t$ and $y$ is the distance $d$.
$\dfrac{87}{1.5}=58$
$\dfrac{130.5}{2.25}=58$
$\dfrac{174}{3} = 58$
Each ratio simplifies to $58$ so the constant of variation is $58$ and $d$ varies directly with $t$.
The function rule is $d = 58t$.
