What is the relationship between the values X and Y in the table below, and what is the corresponding function rule?
table
X } 2 , 4 , 6
Y } 1 , 0 , -1
To find the relationship between the values of X and Y in the table, we can observe any patterns or trends.
Looking at the given values, we can see that as X increases by 2 (2, 4, 6), Y decreases by 1 (1, 0, -1) each time. This suggests that there is a constant rate of change between X and Y.
In terms of a function rule, we can express the relationship between X and Y as:
Y = -X/2 + 2
This rule shows that Y is a linear function of X, and for every increase of 2 in X, Y decreases by 1.
To understand the relationship between the values X and Y in the given table, we can observe the pattern in how the values change.
When X increases by 2 (from 2 to 4), Y decreases by 1 (from 1 to 0).
When X increases by 2 again (from 4 to 6), Y decreases by 1 again (from 0 to -1).
From this pattern, we can deduce that for every increase of 2 in X, Y decreases by 1. This demonstrates a linear relationship between X and Y.
The corresponding function rule for this relationship can be expressed as:
Y = -1/2 * X + b
To determine the value of b, we can substitute one of the pairs of X and Y values from the table into the equation. Let's take the pair (2, 1):
1 = -1/2 * 2 + b
Simplifying this equation, we have:
1 = -1 + b
By adding 1 to both sides of the equation, we find:
b = 2
Therefore, the complete function rule for this relationship is:
Y = -1/2 * X + 2