Question

Help me with the work

Answer 1

Option B k > 0

Explanation:

we know that

Observing the graph

The slope of the line is positive

The y-intercept is negative

we have

`3y-2x=k(5x-4)+6\\ \\3y=5kx-4k+6+2x\\ \\3y=[5k+2]x+(6-4k)\\ \\y=(1)/(3)[5k+2]x+(2-(4)/(3)k)`

The slope of the line is equal to

`m=(1)/(3)[5k+2]`

Remember that the slope must be positive

so

`5k+2> 0\\ \\k > -(2)/(5)`

The value of k is greater than -2/5

Analyze the y-intercept

`(2-(4)/(3)k) < 0\\ \\ 2 < (4)/(3)k\\ \\1.5 < k\\ \\k > 1.5`

1.5 is greater than zero

so

the solution for k is the interval ------> (1.5,∞)

therefore

must be true

k > 0