(-4,-2) (0,0) and (2,7) (k,5) what is k
i have to find the value of k, so that the two lines will be parallel.
The first observation to make is that parallel lines have
the same slope. We can determine the slope of the first line
and use that to find the unknown x value for the second line.
Let's give identities to the points so we can refer to them
by name.
P1 is (x1, y1) (-4,-2)
P2 is (x2, y2) (0, 0)
P3 is (x3, y3) (2, 7)
P4 is (x4, y4) (k, 5)
The x and y designations are so you can follow along with
the general equation to calculate the slope, m.
1) m = (y2 - y1) / (x2 - y2)
2) m = (0 - (-2)) / (0 - (-4))
3) m = (0 + 2) / (0 + 4)
4) m = 2 / 4 = 1/2
Now that we know the slope of the two lines, we can use
the second set of points to find the value of k.
5) m = (y4 - y3) / (x4 - x3) Of couse, x4 is k.
6) m = (5 - 7) / (k - 2)
We know that m is 1/2, so we will now substitute that into
the equation.
1/2 = (5 - 7) / (k - 2)
1/2 = -2 / (k - 2)
We multiply both sides by (k - 2)
1/2 * (k - 2) = (-2 / (k - 2)) * (k - 2)
1/2 * (k - 2) = -2
Multiply both sides by 2
1/2 * (k - 2) * 2 = -2 * 2
(k - 2) = -4
Add 2 to both sides
(k - 2) + 2 = -4 + 2
k = -2
Substitute that value into equation 6, for the slope.
m = (5 - 7) / (k - 2)
m = (5 - 7) / (-2 - 2)
m = -2 / -4
m = 1/2
When k is -2, the second line segment has the same
slope as the first line segment, therefore, the two
lines are parallel.