Answer:
Option B k > 0
Step-by-step explanation:
we know that
Observing the graph
The slope of the line is positive
The y-intercept is negative
we have
[tex]3y-2x=k(5x-4)+6\\ \\3y=5kx-4k+6+2x\\ \\3y=[5k+2]x+(6-4k)\\ \\y=\frac{1}{3}[5k+2]x+(2-\frac{4}{3}k)[/tex]
The slope of the line is equal to
[tex]m=\frac{1}{3}[5k+2][/tex]
Remember that the slope must be positive
so
[tex]5k+2> 0\\ \\k > -\frac{2}{5}[/tex]
The value of k is greater than -2/5
Analyze the y-intercept
[tex](2-\frac{4}{3}k) < 0\\ \\ 2 < \frac{4}{3}k\\ \\1.5 < k\\ \\k > 1.5[/tex]
1.5 is greater than zero
so
the solution for k is the interval ------> (1.5,∞)
therefore
must be true
k > 0
