Question

Find the equation of the line
y=mx+b

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}{-2}~,~\stackrel{y_1}{-7})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{3}-\stackrel{y1}{(-7)}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{(-2)}}} \implies \cfrac{3 +7}{8 +2} \implies \cfrac{ 10 }{ 10 } \implies 1`

`\begin{array}c \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}{(-7)}=\stackrel{m}{ 1}(x-\stackrel{x_1}{(-2)}) \implies y +7 = 1 ( x +2) \\\\\\ y+7=x+2\implies {\Large \begin{array}{llll} y=x-5 \end{array}}`