Question

If A = {( x , y ): (2, -2), (4, -1), (6, 0), . . .}, complete the rule for set A . y=

A) 1/2x - 3
B) -1/2x + 3
C) -1/2x - 1

Answer 1

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.