SOLUTION: If the line represented by the equation 4x+ky-10=0 is parallel to the line with equation 2x-10y+7=0, what is the value of k?

Algebra ->  Linear-equations -> SOLUTION: If the line represented by the equation 4x+ky-10=0 is parallel to the line with equation 2x-10y+7=0, what is the value of k?      Log On


   

Question 1151416: If the line represented by the equation 4x+ky-10=0 is parallel to the line with equation 2x-10y+7=0, what is the value of k?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

If the line represented by the equation
4x%2Bky-10=0+
ky=-4x%2B10+
y=-%284%2Fk%29x%2B10%2Fk+=>slope is m=-%284%2Fk%29
is perpendicular to the line with the equation
2x-10y%2B7=0
2x%2B7=10y
y=%281%2F5%29x%2B7%2F10=>slope is m%5B1%5D=1%2F5
perpendicular lines have slopes negative reciprocal to each other
m=-1%2Fm%5B1%5D
substitute both
-%284%2Fk%29=-1%2F%281%2F5%29.....solve for k
-%284%2Fk%29=-5.......both sides multiply by -1
4%2Fk=5
4=5k
k=4%2F5
so, the value of k is 4%2F5
y=-%284%2F%284%2F5%29%29x%2B10%2F%284%2F5%29+
y=-5x%2B25%2F2+ is perpendicular to y=%281%2F5%29x%2B7%2F10

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-5x%2B25%2F2%2C+%281%2F5%29x%2B7%2F10%29+

Answer by ikleyn(52871) About Me  (Show Source):
You can put this solution on YOUR website!
.
If the line represented by the equation 4x+ky-10=0 is parallel to the line with equation 2x-10y+7=0, what is the value of k?
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            The response by @MathLover1 is written  as if the question is about  PERPENDICULAR  lines;
            but it is about  PARALLEL  lines.

            So I came to fix it. 


The lines are parallel if and only if their slopes are equal.


It gives you this equation / (proportion)


    -4%2Fk = 2%2F10.


Left side of this equation is the slope of the first line;

respectively, right side of the equation is the slope of the second line.


From this proportion,  k = %28%28-4%29%2A10%29%2F2 = -20.    ANSWER