Answer:
B
Step-by-step explanation:
First we simplify the equation:
3y − 2x = k (5x − 4) + 6
3y − 2x = 5k x − 4k + 6
3y = (5k + 2) x − 4k + 6
y = (5k + 2)/3 x + (6 − 4k)/3
The line has a positive slope and negative y-intercept. So:
(5k + 2)/3 > 0
(6 − 4k)/3 < 0
Solving for k in each:
k > -2/5
k > 3/2
k must be greater than -2/5 and 3/2. Since 3/2 is already greater than -2/5, then k must be greater than 3/2.
If k > 3/2, then it's also true that k > 0. So the answer is B.
