Question

Find the equation of the line shown in the graph. Give your answer in slope-intercept form.

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}{-5}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-2)}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{(-5)}}} \implies \cfrac{4 +2}{5 +5} \implies \cfrac{ 6 }{ 10 } \implies \cfrac{ 3 }{ 5 }`

`\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}{(-2)}=\stackrel{m}{ \cfrac{ 3 }{ 5 }}(x-\stackrel{x_1}{(-5)}) \implies y +2 = \cfrac{ 3 }{ 5 } ( x +5) \\\\\\ y+2=\cfrac{ 3 }{ 5 }x+3\implies {\Large \begin{array}{llll} y=\cfrac{ 3 }{ 5 }x+1 \end{array}}`