SOLUTION: If 3x+ky=7 and y=3-4x are two equations of two different lines find “k” if the lines are perpendicular with full steps. Thank you.

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Question 1108704: If 3x+ky=7 and y=3-4x are two equations of two different lines find “k” if the lines are perpendicular with full steps.
Thank you.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39621) About Me  (Show Source):
Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
.
Step 1.  Find the slope of the second line.

         It is  -4.


Step 2.  The slope "m" of the first line must be opposite reciprocal to -4, the slope of the second line.

         It gives you   m = 1%2F4.


Step 3.  Then the equation of the first line must be y = mx + c = %281%2F4%29%2Ax+%2B+c  with some constant value of "c" 

         (for now, any value of "c" does fit, and we will choose it later).


         The last equation is equivalent to 4y = x + 4c,   or   x - 4y = -4c.   (*)


         Multiply both sides of the equation (*) by 3 to get an equivalent equation

         3x - 12y = -12c.   Take c = -7%2F12 to get   3x - 12y = 7.


         Now k = -12  is the value you are looking for.

Illustration:

graph%28+330%2C+330%2C+-5%2C+5%2C+-5%2C+5%2C%0D%0A++++++++++%283x-7%29%2F12%2C+3-4x%0D%0A%29

Plots 3x-12y = 7 (red), y = 3-4x (green)