SOLUTION: Find a value for k so that the line through (k,-10) and (5,-6) is parallel to y= -1/4x + 3

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Question 213181This question is from textbook
: Find a value for k so that the line through (k,-10) and (5,-6) is parallel to y= -1/4x + 3 This question is from textbook

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find a value for k so that the line through (k,-10) and (5,-6) is parallel to y= -1/4x + 3

Step 1. y=-x%2F4%2B3 has a slope m=-1%2F4 and y-intercept of 3.

Step 2. By Definition the slope m is

m=%28y2-y1%29%2F%28x1-x2%29 where m=-1/4 since lines will be parallel

Step 3. Let x1=k and y1=-10 for (k,-10) and x2=5 and y2=-6 for (5,-6)

Step 4. Substitute values in Step 3 into Step 4

m=%28y2-y1%29%2F%28x1-x2%29

m=%28-6-%28-10%29%29%2F%285-k%29=-1%2F4

4%2F%285-k%29=-1%2F4


Now multiply 4(5-k) to get rid of diameters.

%284%2F%285-k%29%29%284%285-k%29%29=-%281%2F4%29%284%285-k%29%29

16=5-k

Add k-16 to both sides to get k

16%2Bk-16=5-k%2Bk-16

k=-11

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J