Equation of a Line Passing Through Two Points

The equation of a line parallel to the y-axis is undefined and returns ∞.
The slope is positive for an upward-sloping line and negative for a downward-sloping line.

\(\normalsize Linear\ equation\ through\ P\ and\ Q\\ \hspace{20px} P(x_1,y_1),\ Q(x_2,y_2) \hspace{20px}y=ax+b={\large\frac{y_2-y_1}{x_2-x_1}}x+{\large\frac{x_2y_1-x_1y_2}{x_2-x_1}}\\ \hspace{20px}PQ=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\ \hspace{20px}\theta=\tan^{\tiny-1}\left({\large\frac{y_2-y_1}{x_2-x_1}}\right)\\\)