SOLUTION: Find k so that the line through (7,2k) and (4,-3) is parallel to the line through (1, k+1) and (3,5)

Algebra ->  Linear-equations -> SOLUTION: Find k so that the line through (7,2k) and (4,-3) is parallel to the line through (1, k+1) and (3,5)      Log On


   

Question 1129389: Find k so that the line through (7,2k) and (4,-3) is parallel to the line through (1, k+1) and (3,5)
Found 3 solutions by solver91311, MathLover1, MathTherapy:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Lines are parallel ONLY when their slopes are equal. Use the slope formula:



To write two expressions in terms of to represent the slopes of the two lines. Set these two expressions equal to each other and then solve the resulting equation for .


John

My calculator said it, I believe it, that settles it

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Find k so that the line through (7,2k) and (4,-3) is parallel to the line through (1, k%2B1) and (3,5)

use a slopes:
a slope of the line through (7,2k) and (4,-3) is:
m=%28-3-2k%29%2F%284-7%29
m=%28-3-2k%29%2F%28-3%29
a slope of the parallel to the line that passes through (1, k+1) and (3,5) is:
m%5Bp%5D=%285-%28k%2B1%29%29%2F%283-1%29
m%5Bp%5D=%285-%28k%2B1%29%29%2F2
m%5Bp%5D=%285-k-1%29%29%2F2
m%5Bp%5D=%284-k%29%29%2F2


since parallel lines have same slope, we have:
m=m%5Bp%5D
%28-3-2k%29%2F%28-3%29=%284-k%29%2F2....cross multiply
2%28-3-2k%29=%28-3%29%284-k%29
-6-4k=-12%2B3k
-6%2B12=4k%2B3k
6=7k
k=6%2F7
so, slope is
m=%28-3-2%286%2F7%29%29%2F%28-3%29
m=%28-3-12%2F7%29%2F%28-3%29
m=11%2F7
same for parallel line
m%5Bp%5D=%2811%2F7%29
then, points and slope for one line are:

(7,2%286%2F7%29) and (4,-3)
=>(7,12%2F7) and (4,-3)


equation of this line is: use point-slope formula
y-y%5B1%5D=m%28x-x%5B1%5D%29.......if (4,-3)
y-%28-3%29=%2811%2F7%29%28x-4%29
y%2B3=%2811%2F7%29x-%2811%2F7%294
y=%2811%2F7%29x-44%2F7-3
y=%2811%2F7%29x-44%2F7-21%2F7
y=%2811%2F7%29x-65%2F7-> one line

equation of the parallel line is: use point-slope formula
(1, 6%2F7%2B1) and (3,5)
=> (1, 13%2F7) and (3,5)
y-y%5B1%5D=m%28x-x%5B1%5D%29.......if m%5Bp%5D=%2811%2F7%29and (3,5)
y-5=%2811%2F7%29%28x-3%29
y-5=%2811%2F7%29x-%2811%2F7%293
y-5=%2811%2F7%29x-33%2F7
y=%2811%2F7%29x-33%2F7%2B5
y=%2811%2F7%29x-33%2F7%2B35%2F7
y=%2811%2F7%29x%2B2%2F7-> parallel line

=>(7,12%2F7) and (4,-3)
=> (1, 13%2F7) and (3,5)





Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Find k so that the line through (7,2k) and (4,-3) is parallel to the line through (1, k+1) and (3,5)
The other person must be answering a different problem, because all you need to do here is use the slope formula, then set the slopes

equal to each other, which will allow you to determine the value of k.

This person seems to do a TON of UNNECESSARY calculations when these problems are so, so SIMPLE to figure out.

Slope formula: matrix%281%2C3%2C+m%2C+%22=%22%2C+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29%29

We therefore get:  

3(k - 4) = - 2(2k + 3) ------- Cross-multiplying

3k - 12 = - 4k - 6

3k + 4k = - 6 + 12

7k = 6

highlight_green%28matrix%281%2C3%2C+k%2C+%22=%22%2C+6%2F7%29%29

THAT"S ALL!! NOTHING more, NOTHING less!!!