Final answer:
The rule for set A is represented by the linear equation y = (1/2)x - 3, as it fits the pattern of the given points.
Step-by-step explanation:
To determine the rule for set A given as A = {(x, y): (2, -2), (4, -1), (6, 0), ...}, we must find a linear equation that represents the relationship between the x and y values of the ordered pairs.
Let us examine the given points. We see that as the x value increases by 2, the y value increases by 1:
- From (2, -2) to (4, -1), x increases by 2 and y increases by 1.
- From (4, -1) to (6, 0), x increases by 2 and y increases by 1.
This pattern suggests a linear relationship with a slope of 1/2. Now, we need to find the y-intercept. When x = 2, y = -2. Plugging these values into the equation y = (1/2)x + b, we get:
-2 = (1/2)×2 + b
-2 = 1 + b
-3 = b
Thus, the equation following the pattern is y = (1/2)x - 3.