Yes, the function is linear, and the slope is -2.
Is this function linear?
A general linear function is written as:
y = a*x + b
We can see that for fixed increments of x, we also have fixed changes of y.
If we look at our table, we can see that x increases by 1 unit in each row.
While y decreases by 2 units in each row, so we have fixed changes, which means that the relation is linear.
To find the slope, remember that if a line passes through two points (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Here we can use the first two points:
(1, -4) and (2, -6)
Then we will get:
a = (-6 + 4)/(2 - 1) = -2/1 = -2
The slope is -2.