Question

the line passing through the points A (-1,3k) and B (k , 3) is parallel to the line whose equation is 2y+3x=9. write down the co-ordinates of A and B​

Answer 1

k = 3

Explanation:

If the line passing through the points A (-1,3k) and B (k , 3) is parallel to the line whose equation is 2y+3x=9, then their slopes are equal

For coordinate AB;

slope m1 = 3 - 3k/k-(-1)

m1 = 3-3k/k+1

For the line 2y+3x = 9

2y = -3x + 9

y = -3/2 x + 9/2

Slope m2 = -3/2

Since m1 = m2

3-3k/k+1 = -3/2

Cross multiply

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

Expand

6 - 6k = -3k - 3

-6k+3k = -3 - 6

-3k = -9

k = -9/-3

k = 3

Hence the value of k is 3