Find parametric equations for the line that passes through the

Step 1
The given equation of line
${\displaystyle y=\frac{-7}{2}x-2}$
comaparing with the ${\displaystyle y=mx+b}$, we get
${\displaystyle m=\frac{-7}{2}}$ and ${\displaystyle b=-2}$
The slope of the line is ${\displaystyle \frac{-7}{2}}$
Given that the line passes through the point ${\displaystyle (5,2)}$ is parallel to the line ${\displaystyle y=\frac{-7}{2}x-2}$
We know that the slope of parallel line is same
So, the line passes trough the point ${\displaystyle (5,2)}$ has slope ${\displaystyle m=\frac{-7}{2}}$
Step 2
${\displaystyle u\sin g}$ point slope formula,
${\displaystyle y-y_1=m(x-x_1)}$
Here ${\displaystyle m=\frac{-7}{2},(x_1,y_1)=(5,2)}$
${\displaystyle \Rightarrow y-2=\frac{-7}{2}(x-5)}$
${\displaystyle \Rightarrow \frac{y-2}{-7}=\frac{x-5}{2}=t(\le t)}$
Now, $$\begin{gathered} \frac{y-2}{-7}=t \\ \Rightarrow y-2=-7t \\ \Rightarrow y=2-7t \end{gathered}$$
and $\frac{x-5}{2}=t$
$$\begin{gathered} \Rightarrow x=2t \\ \Rightarrow x=5+2t \end{gathered}$$
so, parametric equations for the line that passes through the point ${\displaystyle (5,2)}$ is
$y=2-7t,x=5+2t$
This is the required answer.