Find the y-intercept of the line through (5,7) that is perpendicular to x-3y=6

Question

Find the y-intercept of the line through (5,7) that is perpendicular to x-3y=6

Answer 1

Perpendicular lines have slopes that are the negative inverse of each other [that is, m and (-1/m)].

 

The slope of the line Ax+By=C is (-A/B).  The slope of line x-3y=6 is (1/3).

 

The slope of the perpendicular line is (-3/1) and the line is 3x+y = D.  We need point (5,7) to find D.

     3(5)+7=D

        22 = D

 

The line is:  3x + y = 22    (Standard Form since original line is in Standard Form)

 

The y-intercept [the point where x=0] is (D/B), which is (22/1), or the point (0,22).

Answer 2

 

x - 3 y = 6 

- 3 y = - x + 6

y = 1/3 x - 2     this is one line

 

the another line perpendicular to  y = 1/3 x - 2  

we know the another line like this: y = - 3 x + b (b is the y-intercept)

 

because the another line through (5 , 7), then 

 

7 = -3 * 5 + b

b = 22

 

the line is y = -3 x + 22 which perpendicular to x - 3y = 6