Use an equation to find the value of k so that the line that passes through (-4, k) (-4, k) and (6, - 7) has a slope of m = - 1/5.

The value of k is - 5.

Step-by-step explanation:

To find the value of k, start by using the known information we have in the equation for slope. The equation is below.

m (slope) = (y2 - y1) / (x2 - x1)

In this equation, the first ordered pair would be (x1, y1) and the second would be (x2, y2). So we put the values in for these variables and we get.

-1/5 = (-7 - k) / (6 + 4)

-1/5 = (-7 - k) / 10

Now we can use cross multiplication to solve for k.

-1/5 = (-7 - k) / 10

-1*10 = 5 (-7 - k)

-10 = - 35 - 5k

25 = - 5k

-5 = k

k=-5

Step-by-step explanation:

To find the value of k, start by using the known information we have in the equation for slope. The equation is below.

m (slope) = (y2 - y1) / (x2 - x1)

In this equation, the first ordered pair would be (x1, y1) and the second would be (x2, y2). So we put the values in for these variables and we get.

-1/5 = (-7 - k) / (6 + 4)

-1/5 = (-7 - k) / 10

-1/5 = (-7 - k) / 10

-1*10 = 5 (-7 - k)

-10 = - 35 - 5k

25 = - 5k

-5 = k