Question

The slope of the line is __

The y-intercept is ___

The equation for the line is __

Answer 1

Check the picture below.

to get the equation of any straight line, we simply need two points off of it, let's use those in the picture below

`(\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-3)}}} \implies \cfrac{3 +2}{0 +3} \implies \cfrac{5 }{ 3 }`

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