SOLUTION: Find k so that the line through (5,-2) and(k,2) is parallel to 16x+21y=42

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Question 1184566: Find k so that the line through (5,-2) and(k,2) is parallel to 16x+21y=42
Found 3 solutions by josgarithmetic, MathTherapy, robertb:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
Left Side member must be unchanged, to keep the same slope, because you said you want line which is parallel. Better way is setup the slope from inspecting the given equation.

slope,


Now you can make and you can solve and finish.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Find k so that the line through (5,-2) and(k,2) is parallel to 16x+21y=42
Pay NO ATTENTION to the response from the other person.
You'll NEVER get the correct answer with his "interpretation" of the required equation's slope, namely!
                   

Slope of parallel line, or  

Line through points (5, - 2) and (k, 2) also has a slope (m) of 
                                      
                                       We then get: 
   4(k - 5) = - 21 ------- Cross-Multiplying
    4k - 20 = - 21
         4k = - 1
         

CORRECTED!
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!

It is rather strange that two tutors make the same calculational mistake: One made the error at the highlighted parts --

.

That said, a correct solution is as follows:

Since the line is supposed to be parallel, it must be of the form

, for some constant C.

Since (5,-2) is on this line, ===> ===> C = 38.

===> is the desired parallel line.

Since (k,2) is also on this line, ===> ===> .
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