Determine k so that the given line will have to given slope. 1) 12x - ky = 5, m = 3 2) (-4,k) & (-1,3k), m = 4 3) kx + 2y = 6, m= k+1 4) (k+

4) (k+1, k) & (-3, 2), m= 2

So we have

[2 - k] / [ -3 - (k +1)]  =  2      simplify

[2 - k ] / [-4 - k]  = 2    which we can write as  [k - 2]/ [4 + k] = 2     

Multiply both sides by 4 + k

k - 2 =  8 + 2k      rearrange

-10  = k

1) 12x - ky = 5, m = 3

Rewrite as    ky = 12x - 5    .....divide both sides by k....... y = (12/k) - 5/k  ....and the slope is determined by the coefficient on x....so.....  m = 3  = 12/k    and it's clear that k must be 4

Heres the graph of  12x - 4y = 5 ....... https://www.desmos.com/calculator/ibpwuqrgk0

2) (-4,k) & (-1,3k), m = 4

So we have.....

[3k - k] / [ -1 - (-4)]  = 4

[2k] / [3 ] = 4      multiply both sides by 3

2k  = 12      divide both sides by 2

k = 6

3) kx + 2y = 6, m= k+1

Rewrite as     2y  = -kx + 6   .....divide both sides by 2 .......  y = (-k/2)x + 3

And if the slope = k + 1.....then this implies that   -k/2  = k + 1   

Multiply both sides by 2

-k = 2k + 2   rearrange

-3k = 2    divide both sides by -3   and k = -2/3