Find k to both parts of question

Question

Find k so that the line through (3,-2) (k,1) is a. parallel to 15x+16y=32 b. perpendicular to 2x+3y=6

Answer 1

(a)

 

To be parallel to 

 

15x + 16y = 32, 

 

the slope must be 

 

m = -15/16

 

-15/16 = (-2 - 1) / (3 - k)  = -3 / (3 - k)

 

15/16 = 3 / (3 - k)

 

Can you find k from here?

 

(b)

 

To be perpendicular to

 

2x + 3y = 6,

 

the slope must be

 

m = -1/(-2/3) = 3/2

 

3/2 = (-2 - 1)/(3 - k)

 

3/2 = 3/(k - 3)

 

Can you find k from here?