Question

what is the formula for calculating a slope and what is its magnitude?

Answer 1

$$\begin{gathered} \mathrm{For}\mathrm{calculating}\mathrm{the}\mathrm{slope}\mathrm{of}\mathrm{a}\mathrm{linear}\mathrm{equation} \\ \mathrm{Let}2\mathrm{x}+4\mathrm{y}=8\dots \left(1\right) \\ \mathrm{slope}=\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}\dots \left(2\right) \\ \mathrm{Where}\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)\&\left({\mathrm{x}}_2,{\mathrm{y}}_2\right)\mathrm{are}\mathrm{points}\mathrm{satisfying}\mathrm{the}\mathrm{linear}\mathrm{equation} \\ \mathrm{put}{\mathrm{x}}_1=0\mathrm{in}\mathrm{eq}\left(1\right)\mathrm{we}\mathrm{get}{\mathrm{y}}_1=2\Rightarrow \left({\mathrm{x}}_1,{\mathrm{y}}_1\right)=\left(0,2\right) \\ \mathrm{put}{\mathrm{y}}_2=0\mathrm{in}\mathrm{eq}\left(1\right)\mathrm{we}\mathrm{get}{\mathrm{x}}_2=4\Rightarrow \left({\mathrm{x}}_2,{\mathrm{y}}_2\right)=\left(4,0\right) \\ \mathrm{Now},\mathrm{putting}\mathrm{these}\mathrm{values}\mathrm{in}\mathrm{eq}\left(2\right) \\ \mathrm{slope}=\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_1}=\frac{0-2}{4-0}=\frac{-2}{4}=\frac{-1}{2}\mathrm{Answer} \end{gathered}$$