The data in the table illustrates a linear function.

x, -3,0,3,6,
y, -6,-2,2,6

what is the slope of the linear function

Did you notice that for every 3 units of change in the x's (the run), the y's (the rise) increase by 4 ?

To determine if the data in the table illustrates a linear function, we will need to look for a consistent pattern between the x-values and corresponding y-values.

In a linear function, each change in the x-value will produce a consistent change in the y-value. This consistent change is known as the slope of the linear function.

To find the slope, we can select any two points from the table and apply the slope formula:

slope (m) = (change in y) / (change in x) = (y2 - y1) / (x2 - x1)

Let's choose the points (-3, -6) and (0, -2) from the table:

slope (m) = (-2 - (-6)) / (0 - (-3))
= (-2 + 6) / (0 + 3)
= 4 / 3

Now, let's check if the same slope is found for the other sets of points (-2, 0), (3, 2), and (6, 6).

(-2, 0) and (0, -2):
slope (m) = (-2 - 0) / (0 - (-2))
= -2 / 2
= -1

(0, -2) and (3, 2):
slope (m) = (2 - (-2)) / (3 - 0)
= 4 / 3

(3, 2) and (6, 6):
slope (m) = (6 - 2) / (6 - 3)
= 4 / 3

As we can see, the slope of the linear function is consistently 4/3 across all sets of points. Therefore, the data in the table illustrates a linear function.