Question

Complete the equation of the line through ( 3 , − 1 ) (3,−1)left parenthesis, 3, comma, minus, 1, right parenthesis and ( 4 , 7 ) (4,7)left parenthesis, 4, comma, 7, right parenthesis. Use exact numbers.

Answer 1

`(\stackrel{x_1}{3}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{7}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{3}}} \implies \cfrac{ 7 +1 }{ 1 } \implies 8`

`\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}{(-1)}=\stackrel{m}{8}(x-\stackrel{x_1}{3}) \implies y +1 = 8 ( x -3) \\\\\\ y+1=8x-24\implies {\Large \begin{array}{llll} y=8x-25 \end{array}}`