Question

A functionf(x) is graphed on the coordinate plane.

What is the function rule in slope-intercept form?

Enter your answer in the box.

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}{-2}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-2)}}} \implies \cfrac{-3}{4 +2} \implies \cfrac{ -3 }{ 6 } \implies - \cfrac{1 }{ 2 }`

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