Question 213181
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/4+3}}} has a slope {{{m=-1/4}}} and y-intercept of 3.


Step 2.  By Definition the slope m is


{{{m=(y2-y1)/(x1-x2)}}}  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=(y2-y1)/(x1-x2)}}}


{{{m=(-6-(-10))/(5-k)=-1/4}}}


{{{4/(5-k)=-1/4}}}



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


{{{(4/(5-k))(4(5-k))=-(1/4)(4(5-k))}}}


{{{16=5-k}}}


Add k-16 to both sides to get k


{{{16+k-16=5-k+k-16}}}


{{{k=-11}}}


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J