P (-1, 2)
Q (k, -4)
m= -1/2
determine k so that the line through the given points will have slope m.
how do you do this?
Formula of a slope is (y2-y1)/(x2-x1)
K is your variable for x2
Substitute:
2- -4 (or 2+4) divided by -1-k
Set the equation and solve for "k":
6/(-1-k) = -1/2
6 = (1+k)/2
12 = 1+k
k = 11
x1*
Excuse me. k is your variable for x1 the way I set it up.
To determine the value of k so that the line through the points P(-1, 2) and Q(k, -4) will have a slope of -1/2, we can use the slope formula.
The slope formula is given as:
m = (y2 - y1) / (x2 - x1)
Here, (x1, y1) represents the coordinates of point P, and (x2, y2) represents the coordinates of point Q. In our case, (x1, y1) = (-1, 2) and (x2, y2) = (k, -4).
Substituting these values into the slope formula, we have:
-1/2 = (-4 - 2) / (k - (-1))
Simplifying the equation further, we have:
-1/2 = -6 / (k + 1)
To solve for k, we can cross-multiply:
-1(k + 1) = 2(-6)
-k - 1 = -12
Adding 1 to both sides, we get:
-k = -11
Finally, multiplying both sides by -1, we find:
k = 11
Therefore, the value of k for the line passing through P(-1, 2) and Q(k, -4) with a slope of -1/2 is k = 11.