Question

Find an equation for the line with the given properties. Perpendicular to the line - 2x + 9y = - 39 containing the point (- 3, - 8)

Answer 1

`9 x+2 y +43 =0`

Explanation:

Step 1:-

Given line -2 x +9 y = -39 can be written as

`9 y = -39 +2 x`

`y = (2 x)/(9) - (39)/(9)`...........(1)

comparing above equation y=m x+c

here
`m = (2 )/(9) and y-intercept  is c = (-39)/(9)`

Step 2:-

Perpendicular line condition:-

two lines are perpendicular then their slopes are reciprocal

`m_(2) = (-1)/(m_(2) )`

`m_(1)m_(2) = -1`

`[tex]m_(2) = (-1)/((2)/(9)  )`[/tex]

slope of the perpendicular line is

`m_(2) = (-9)/(2)`

Step 3:-

The equation of the perpendicular line is

`y-y_(1) = (-1)/(m_(1) ) (x-x_(1))`

`y-(-8)=(-9)/(2) (x+3)`

`2 y +16 = -9 x -27`

simplify
`9 x+2 y +16+27=0`

Final answer :-

The equation of the perpendicular line is

`9 x+2 y+43=0`