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.