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

Find an equation for the line with the given properties.

gagem1278

15.01.2022

9 x+2 y +43 =0

Step-by-step explanation:

Step 1:-

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

9 y = -39 +2 x

$y = \frac{2 x}{9} - \frac{39}{9}$ ...........(1)

comparing above equation y=m x+c

here $m = \frac{2 }{9} and y-intercept is c = \frac{-39}{9}$

Step 2:-

Perpendicular line condition:-

two lines are perpendicular then their slopes are reciprocal

$m_{2} = \frac{-1}{m_{2} }$

$m_{1}m_{2} = -1$

slope of the perpendicular line is

$m_{2} = \frac{-9}{2}$

Step 3:-

The equation of the perpendicular line is

$y-y_{1} = \frac{-1}{m_{1} } (x-x_{1})$

$y-(-8)=\frac{-9}{2} (x+3)$

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

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