Question

Complete the equation of the line through ( − 8 , 8 ) and ( 1 ,− 10 ). Use exact numbers.

Answer 1

`(\stackrel{x_1}{-8}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-10}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{1}-\underset{x_1}{(-8)}}} \implies \cfrac{ -18 }{1 +8} \implies \cfrac{ -18 }{ 9 } \implies -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}{8}=\stackrel{m}{-2}(x-\stackrel{x_1}{(-8)}) \implies y -8 = -2 ( x +8) \\\\\\ y-8=-2x-16\implies {\Large \begin{array}{llll} y=-2x-8 \end{array}}`

Answer 2

y = - 2x - 8

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

let (x₁, y₁ ) = (- 8, 8 ) and (x₂, y₂ ) = (1, - 10 )

substitute these values into the formula for m

m =
`(-10-8)/(1-(-8))` =
`(-18)/(1+8)` =
`(-18)/(9)` = - 2 , then

y = - 2x + c ← is the partial equation

to find c , substitute either of the 2 points into the partial equation

using (- 8, 8 )

8 = - 2(- 8) + c = 16 + c ( subtract 16 from both sides )

- 8 = c

y = - 2x - 8 ← equation of line