Question

Find the equation of the line shown.

I
У.
#&+
4
3
21
of du & u
4
2
3
-5
2 3 4 5
X

Answer 1

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

`(\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-4)}}} \implies \cfrac{-2}{4 +4} \implies \cfrac{ -2 }{ 8 } \implies - \cfrac{ 1 }{ 4 }`

`\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}{3}=\stackrel{m}{- \cfrac{ 1 }{ 4 }}(x-\stackrel{x_1}{(-4)}) \implies y -3 = - \cfrac{ 1 }{ 4 } ( x +4) \\\\\\ y-3=- \cfrac{ 1 }{ 4 }x-1\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 4 }x+2 \end{array}}`