Question

Find the slope and inclination of the line through each pair of the following points :(-1,-8)(5,7).

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that},\mathrm{slope}\mathrm{of}\mathrm{the}\mathrm{line}\mathrm{segment}\mathrm{joining}\mathrm{the}\mathrm{points}\left(x_1,y_1\right)\mathrm{and}\left(x_2,y_2\right)\mathrm{is}\mathrm{given}\mathrm{by}, \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \mathrm{Now},\mathrm{slope}\mathrm{of}\mathrm{the}\mathrm{line}\mathrm{segment}\mathrm{joining}\left(-1,-8\right)\mathrm{and}\left(5,7\right)\mathrm{is} \\ m=\frac{7+8}{5+1}=\frac{15}{6}=\frac{5}{2} \\ \mathrm{Now},\boxed{\mathrm{slope},\mathrm{m}=\frac{5}{2}} \\ \mathrm{Let}\mathrm{\theta }\mathrm{be}\mathrm{the}\mathrm{inclination}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{line}. \\ \mathrm{Now},m=\tan \theta \\ \Rightarrow \tan \theta =\frac{5}{2} \\ \Rightarrow \boxed{\theta ={\tan }^{-1}\left(\frac{5}{2}\right)} \end{gathered}$$