Question

The point (-2, y) is on the same line as the points (1, 2) and (7, -1). What is the value of y?

Answer 1

Step-by-step explanation: (-2, y) (1, 2) and (7, -1) wat is the value of y

Answer 2

that means that the slope for all three points is the same, since all are collinear, hmmm what's the slope of (1 , 2) and (7 , -1)?

`(\stackrel{x_1}{1}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{1}}} \implies \cfrac{ -3 }{ 6 } \implies - \cfrac{1 }{ 2 }`

ahaaa!, that means from from (-2 , y) and either of those points is the same slope of -1/2, so

`(\stackrel{x_1}{-2}~,~\stackrel{y_1}{y})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-1})`

`\stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-1}-\stackrel{y1}{y}}}{\underset{\textit{\large run}} {\underset{x_2}{7}-\underset{x_1}{(-2)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{ \cfrac{ -1 }{ 2 }}\implies \cfrac{-1-y}{7+2}=\cfrac{-1}{2}\implies \cfrac{-1-y}{9}=\cfrac{-1}{2} \\\\\\ -2-2y=-9\implies -2y=-7\implies y=\cfrac{-7}{-2}\implies y=\cfrac{7}{2}`