find the value of k if the line through the points (2k+1,-4) and (5,3-k) is parallel to the line trough the points (-4,-9) and ( 2,-3)

Question

find the value of k if the line through the points (2k+1,-4) and (5,3-k) is parallel to the line trough the points (-4,-9) and ( 2,-3)

Answer 1

The slope of the line through (-4,-9) and (2,-3) is (-9 - -3) / (-4 -2) = (-6)/(-6) = 1

Since they are parallel, the slopes MUST be the same.

(3-k) - -4 = 3-k + 4 = 7-k is the numerator of the slope

5 - 2k - 1 = 4 - 2k is the denominator of the slope

(7-k)/(4-2k ) = 1

7-k = 4 - 2k

7+k = 4

k = -3

Answer 2

Greetings! Lets solve this shall we ?

So, we must find the value of k using the given information. We have to find the equation of a line with the given points (-4,-9) and (2,-3) first before we can find the value of k. Now, we find the slope such that

m = (-3-(-9)) / (2-(-4)) = 6 / 6 = 1. Then we yields the point-slope formula to find the equation of a line such that

y - y1 = m(x - x1)

y - (-9) = (1)(x - (-4))

y + 9 = x + 4

y = x - 5

The other given points with k involved has to give a line parallel to y = x - 5 where the slope must be the same m = 1 such that

m = [(3-k) - (-4)] / [5 - (2k+1)] = 1

(7-k) / (4-2k) = 1............Then we cross multiply to get

7 - k = 4 - 2k............Then we solve for k by first adding 2k to the other side such that

7 + k = 4.............Then subtract 7 to the other side such that

k = -3

I hope this helped!