Find the rule for the mapping given the following pairs (x, y): (-5, -5), (-3, 0), (-1, 5), (1, 10), (3, 15), (5, 20).

Observe the pattern in x values: -5, -3, -1, 1, 3, 5. Each x value increases by 2.
Observe the pattern in y values: -5, 0, 5, 10, 15, 20. Each y value increases by 5.
Since there is a constant change, this is a linear relationship of the form y = mx + c.

The slope m is the ratio of the change in y to the change in x.
m = (change in y) / (change in x)
m = 5 / 2

Now we have the equation y = (5/2)x + c.
Let's use the point (-5, -5) to find c:
-5 = (5/2)(-5) + c
-5 = -25/2 + c
Add 25/2 to both sides:
c = -5 + 25/2
c = -10/2 + 25/2
c = 15/2

Substitute the values of m and c into y = mx + c:
y = (5/2)x + 15/2

Let's verify with another point, for example (1, 10):
y = (5/2)(1) + 15/2
y = 5/2 + 15/2
y = 20/2
y = 10
This matches the given point.

The rule for the mapping is:
y = (5/2)x + 15/2