Answer
$ y-y_1=\dfrac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)$; Point-slope Equation
Work Step by Step
Re-arrange the parametric equations as shown below:
$ t=\dfrac{x-x_1}{x_2-x_1}$ and $ t=\dfrac{y-y_1}{y_2-y_1}$
Now, $\dfrac{x-x_1}{x_2-x_1}=\dfrac{y-y_1}{y_2-y_1}$
$\implies y-y_1=\dfrac{(x-x_1)(y_2-y_1)}{(x_2-x_1)}$
$\implies y-y_1=\dfrac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)$
Therefore, $ y-y_1=\dfrac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)$; Point-slope Equation
