Question

What is the equation of line N?

Give your answer in the form y=mx+c,where m and c are integers or fractions in their simplest forms

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}{-3}~,~\stackrel{y_1}{-25})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-10}-\stackrel{y1}{(-25)}}}{\underset{\textit{\large run}} {\underset{x_2}{-2}-\underset{x_1}{(-3)}}} \implies \cfrac{-10 +25}{-2 +3} \implies \cfrac{ 15 }{ 1 } \implies 15`

`\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}{(-25)}=\stackrel{m}{15}(x-\stackrel{x_1}{(-3)}) \implies y +25 = 15 ( x +3) \\\\\\ y +25 = 15 x +45 \implies {\Large \begin{array}{llll} y = 15 x +20 \end{array}}`