Answer
$$
\frac{d y}{d x} =\frac{7}{2}
$$
and at $t=1$, we have
$$
\frac{d y}{d x}= \frac{7}{2}.
$$
Work Step by Step
Since $x=2t+9$ and $y=7t-9$ then we have
$$
\frac{d y}{d x}=\frac{d y / d t}{d x / d t}=\frac{y^{\prime}(t)}{x^{\prime}(t)}=\frac{7}{2}=
$$
and at $t=1$, we have
$$
\frac{d y}{d x}= \frac{7}{2}.
$$
