## Precalculus (6th Edition) Blitzer

$y-y_1=\dfrac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)$; Point-slope Equation
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