find the value of k such that the lines whose equations are 3x+5ky=7 and 9kx+8y=15 are parallel.
the lines are:
3x + 5ky = 7
9kx + 8y = 15
Convert both these eqns into the form: y = mx + c
In this form, m is the gradient of the line and c is the y-intercept.
In this form, our lines are,
3x + 5ky = 7 --> y = -(3/5k)x - (7/5k) i.e. m1 = -(3/5k)
9kx + 8y = 15 --> y = -(9k/8)x - (15/8) i.e. m2 = -(9k/8)
The two lines are parallel when they have the same gradient, i.e. m1 = m2
So, 3/5k = 9k/8
24 = 45k^2
8 = 15k^2
k = sqrt(8/15)