Question

Find the equation of a line that passes through the point (2,-4) and has a gradient of -5. Leave your answer in the form y = m x + c

Answer 1

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

`(\stackrel{x_1}{2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 5 \\\\\\ \begin{array} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 5}(x-\stackrel{x_1}{2}) \implies y +4= -5 (x -2) \\\\\\ y+4=-5x+10\implies {\Large \begin{array}{llll} y=-5x+6 \end{array}}`