Question

What is the slope, y intercept and equation

Answer 1

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

`(\stackrel{x_1}{1}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{4 +2}{3 -1} \implies \cfrac{ 6 }{ 2 }\implies 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}{3}(x-\stackrel{x_1}{1}) \implies y +2= 3 (x -1) \\\\\\ y+2=3x-3\implies {\LARGE \begin{array}{llll} y=3x\underset{(0~~,~~-5)}{\stackrel{\stackrel{y-intercept}{\downarrow }}{-5}} \end{array}}`