Question

-10

Complete the equation for the line
shown in the graph.
(-1,-2)
(1,4)
(0, 1)
y=[?]x + [ ]

Answer 1

to get the equation of any straight line, we simply need two points off of it, let's use two from the picture above, say hmmm (-1 , -2) and (1 , 4)

`(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{1}~,~\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}{1}-\underset{x_1}{(-1)}}} \implies \cfrac{4 +2}{1 +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+1 \end{array}}`