Answer:
k = -3
Step-by-step explanation:
A parallel line will have the same slope as the referenced line. The reference line is defined by the 2 points (-4,-9) and (2,-3). The slope of this line is it's Rise/Run:
Rise = (-3 -(-9)) = 6
Run = (2 - (-4)) = 6
The slope is 6/6 or 1. This equation can be written as y = 1x +b. To find b, use one of the two points [I'll use (2,-3)] and solve for b:
y = x + b
-3 = 2 + b
b = -5
The equation is y = x - 5
The line parallel to this line will also have a slope of 1, so it can be written as y = x + b. We now need to find a value of b such that the two points (2k+1, -4) and (5, 3-k) will both be on the line. Use one of the points in the equation [I'll use (5, 3-k)]:
y = x + b
(3-k) = 5 + b
b = -(2+k)
Now use that value of b with the other point (2k+1, -4):
y = x - (2+k)
-4 = (2k+1) - (2+k)
-4 = 2k + 1 - 2 - k
-4 = k - 1
k = -3
The equation of the parallel line is:
y = x - (2 + k) [k = -3]
y = x - (2 - 3)
y = x + 1
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(2k + 1,-4) now becomes (2(-3) + 1) or (-5,-4)
(5,3-5) becomes (5, 3-(-3)) or (5, 6)
The two points are:
(-5,-4) and
(5, 6)
-===
Plot the parallel equation and add the two points (-5,-4) and (5,6).
See attached graph.
You'll see that the new line is parallel to the reference line and that both points lie on it, based on k having the value -3.
