Answer:
2nd quadrant.
Step-by-step explanation:
The given function is
[tex]h(x)=-6+\dfrac{2}{3}x[/tex]
We need to find the quadrant from which the graph of function is not passing.
At x=0,
[tex]h(0)=-6+\dfrac{2}{3}(0)=-6[/tex]
So, y-intercept is (0,-6).
At h(x)=0,
[tex]0=-6+\dfrac{2}{3}x[/tex]
[tex]6=\dfrac{2}{3}x[/tex]
[tex]18=2x[/tex]
[tex]9=x[/tex]
So, x-intercept is (9,0).
It means the graph intersect negative side of y-axis and positive side of x-axis. When we join these two points, we get the graph is not passing through the 2nd quadrant.
Therefore, the required quadrant is 2nd quadrant.
