Question

Help me with the work

Answer 1

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

$3y-2x=k(5x-4)+6\\ \\3y=5kx-4k+6+2x\\ \\3y=[5k+2]x+(6-4k)\\ \\y=\frac{1}{3}[5k+2]x+(2-\frac{4}{3}k)$

The slope of the line is equal to

$m=\frac{1}{3}[5k+2]$

Remember that the slope must be positive

so

$5k+2> 0\\ \\k > -\frac{2}{5}$

The value of k is greater than -2/5

Analyze the y-intercept

$(2-\frac{4}{3}k) < 0\\ \\ 2 < \frac{4}{3}k\\ \\1.5 < k\\ \\k > 1.5$

1.5 is greater than zero

so

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

therefore

must be true

k > 0