Write a function rule for the data in the table. determine if it's a direct variation, inverse variation or neither. last, determine the value of x if y=10.

I'm assuming you meant to say "graph" instead of "table".

The function rule is y = x+2 because the y intercept is 2, where the graph crosses the y axis. The slope is 1 meaning we move 1 unit up and 1 unit to the right each time. You can use the slope formula to determine the slope, or simply make this observation of rise vs run.

Because this line doesn't go through the origin, and because it's not in the form y = k*x, this means we do not have a direct variation equation.

We do not have an inverse variation equation either because it is not in the form y = k/x or x*y = k. A visual indication of this is that the graph isn't a curved hyperbola.

Therefore, this function is neither direct variation nor inverse variation

Plug in y = 10 and solve for x

y = x+2

x+2 = y

x+2 = 10

x+2-2 = 10-2

x = 8

The value of x is 8

So if x = 8, then y = 10 meaning that (x,y) = (8,10) is on this blue diagonal line.