Question

Find the equation of this line. y = [? ]x + []
Simplify your answer and enter as an integer.​

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}{0}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{6}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{0}}} \implies \cfrac{ 6 +2 }{ 4 } \implies \cfrac{ 8 }{ 4 } \implies 2`

`\begin{array}ll \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}{(-2)}=\stackrel{m}{2}(x-\stackrel{x_1}{0}) \implies y +2 = 2 ( x -0) \\\\\\ y+2=2x\implies {\Large \begin{array}{llll} y=2x-2 \end{array}}`