Question

Find an equation for the line that passes through the points (-6,-5) and (6,4)

Answer 1

`(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-6)}}} \implies \cfrac{4 +5}{6 +6} \implies \cfrac{ 9 }{ 12 } \implies \cfrac{3 }{ 4 }`

`\begin{array}ll \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}{(-5)}=\stackrel{m}{ \cfrac{3 }{ 4 }}(x-\stackrel{x_1}{(-6)}) \implies y +5 = \cfrac{3 }{ 4 } ( x +6) \\\\\\ y+5=\cfrac{3 }{ 4 }x+\cfrac{9}{2}\implies y=\cfrac{3 }{ 4 }x+\cfrac{9}{2}-5\implies {\Large \begin{array}{llll} y=\cfrac{3 }{ 4 }x-\cfrac{1}{2} \end{array}}`

Answer 2

`\displaystyle \boxed{ y=(3)/(4)x-(1)/(2) }`

Explanation:

First, we will find the slope. This is done by finding the change in y over the change in x.

`\displaystyle (y_(2) -y_(1) )/(x_(2) -x_(1) )= (4--5)/(6--6) =(4+5)/(6+6)=(9)/(12)=(3)/(4)`

Next, we will find the equation. We will create a point-slope equation and simplify into slope-intercept form.

y - 4 =
`(3)/(4)`(x - 6)

y =
`(3)/(4)`x -
`(9)/(2)` + 4

y =
`(3)/(4)`x -
`(1)/(2)`