On a coordinate plane, a line goes through (negative 4, 4) and (4, negative 2). A point is at (6, 0). What is the equation of the line that is perpendicular to the given line and has an x-intercept of 6? y = –Three-fourthsx + 8 y = –Three-fourthsx + 6 y = Four-thirdsx – 8 y = Four-thirdsx – 6

Respuesta :

y = Four-thirds x – 8

Step-by-step explanation:

Step 1:

   First step is to find the slope of the line joining the 2 given points                                    

   (negative 4, 4) and (4, negative 2).

   Formula for finding the slope of the line joining 2 given points is

  Slope m  =   (change in y)/(change in x)  

   Using the above formula , the slope of the line joining the 2 given points  

   is  m = (-2-4)/(4-(-4)) = -6/8 =-3/4

Step 2 :

    Find the slope of the line perpendicular to the line joining the 2 given  

    points

    Slopes of 2 perpendicular lines are negative reciprocals of each other  

    , i.e if m1 and m2 are slopes of 2 lines then m1*m2 = -1, if the lines are

    perpendicular to each other.

    Hence the slope of the line perpendicular to the line joining the above 2

    given points is

     m1*m2 = -1   => (-3/4)*m2 = -1 => m2 = 4/3

Step 3 :

    Find the equation of the line with slope 4/3 and has an x- intercept of 6

     X intercept of 6 means the line passes through the point (6,0)

     Equation of a line passing through a given point and having a slope

     of  m is (y - y1) = m(x-x1).

     Substituting slope as m= 4/3 and point (x1,y1) as (6,0) in the above  

     equation,

      (y-0) = (4/3)(x-6)

       =>   y = (4/3)x - (4/3)*6

       =>   y = (4/3)x - 8

               

Hence the required answer is y = (4/3)x - 8

Answer:

in other words the answer is CCCCCCCCCCCCCCCCCCCCCCCC

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