The slope of the line that passes through the points (7,w) and (4,-6) is 4/3. what is the vaule of w?

Slope is the change in y over the change in x, or

y2-y1/x2-x1

It doesn't matter which x and y coordinates we use as x1 and x2 as long as we are consistent with both. Since the x component in the slope = 3, we can see that they used 7-4, so for the y component we will use w - (-6)

w-(-6) = 4  (we set it to 4 because of the slope)
w+6 = 4
w = 4-6
w = -2

The missing point is -2

Tan (5π/6)
=tan (π-π/6)
=(tan π-tan (π/6))/(1+tan π tan π/6)
=-tan (π/6)
=-1/√3
=-√3/3
Hence the answer is: -√3/3