What is perpendicular to [tex]y = 3x - 9[/tex] and passes through the point (3, 1)?
Answer (3)
To find the equation of a line that is perpendicular to y = 3x - 9 and goes through the point (3,1), we use the negative reciprocal of the original slope (3) which is -1/3 and apply the point-slope equation, resulting in y = (-1/3)x + 2 as the perpendicular line's equation. ;
( 3 , 1 ) , y = 3 x − 9 T h e s l o p e i s : m 1 = 3 I f m 1 an d m 2 a re t h e g r a d i e n t s o f tw o p er p e n d i c u l a r l in es w e ha v e m 1 ⋅ m 2 = − 1 3 ⋅ m 2 = − 1 / : 3 m 2 = − 3 1
\Now yo u r e q u a t i o n o f l in e p a ss in g t h ro ug h ( 3 , 1 ) w o u l d b e : y = m 2 x + b 1 = − 3 1 ⋅ 3 + b
1 = − 1 + b b = 1 + 1 b = 2 y = − 3 1 x + 2
The perpendicular line to y = 3 x − 9 through the point ( 3 , 1 ) has an equation of y = − 3 1 x + 2 . This line has a slope of − 3 1 , which is the negative reciprocal of the original slope 3 .
;
