+0  
 
0
241
1
avatar

Find n so that line is perpendicular to the line with the equation -2y+4=6x+8 through the points at (n,40) and (2, -8)

Guest Oct 26, 2014

Best Answer 

 #1
avatar+17711 
+5

Line will be perpendicular if their slopes are negative reciprocal.

First, find the slope of  -2y + 4  =  6x + 8

                                      -2y  =  6x + 4

                                         y  =  -3x - 2

The slope of this line is  -3  so the slope of any line parallel to it will be  1/3.

Now, find the equation of the line that passes through  (2,-8)  with a slope of  1/3.

Since we know a point and a slope, let's use the point-slope form:  y - y1  =  m(x - x1)

--->   y - -8  =  (1/3)(x - 2)

--->   y  + 8  =  (1/3)(x - 2)

--->   3y + 24  =  x - 2

--->  -x + 3y  =  -26

--->   x - 3y  =  26     <---  This is the equation of the line perpendicular to  y  =  -3x - 2  at the point (2, -8)

To find the value of n of the point  (n, 40), replace y with 40:

        x - 3(40)  =  26

        x - 120  =  26

         x  =  146  =  n

geno3141  Oct 26, 2014
Sort: 

1+0 Answers

 #1
avatar+17711 
+5
Best Answer

Line will be perpendicular if their slopes are negative reciprocal.

First, find the slope of  -2y + 4  =  6x + 8

                                      -2y  =  6x + 4

                                         y  =  -3x - 2

The slope of this line is  -3  so the slope of any line parallel to it will be  1/3.

Now, find the equation of the line that passes through  (2,-8)  with a slope of  1/3.

Since we know a point and a slope, let's use the point-slope form:  y - y1  =  m(x - x1)

--->   y - -8  =  (1/3)(x - 2)

--->   y  + 8  =  (1/3)(x - 2)

--->   3y + 24  =  x - 2

--->  -x + 3y  =  -26

--->   x - 3y  =  26     <---  This is the equation of the line perpendicular to  y  =  -3x - 2  at the point (2, -8)

To find the value of n of the point  (n, 40), replace y with 40:

        x - 3(40)  =  26

        x - 120  =  26

         x  =  146  =  n

geno3141  Oct 26, 2014

17 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details