Question

Write a linear equation that models the data in the table

X Y
-6 0
-3 2
0 4
3 6

Equation:?

Answer 1

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

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