The ordered pairs (−4, −3), (−2, −2), (4,1), (6,2), and (8,3) represent a function. What is a rule that represents this function?
A. y = 1/2x − 1 *****
B. y = −2x − 1
C. y = 2x − 1
D. y = −12x − 1
correct
thanks!!
To find a rule that represents a function, we need to look for patterns or relationships between the x-values and y-values of the given ordered pairs.
Let's first observe the x-values and y-values of the given pairs:
(-4, -3), (-2, -2), (4, 1), (6, 2), (8, 3)
When we compare the x-values and y-values, we can see that as the x-values increase:
- The y-values increase at a constant rate of 1.
Taking the first pair (-4, -3), we can derive the rule:
y = x + (some constant value)
To find the constant value, we can substitute one of the pairs into the equation. Let's use (-4, -3):
-3 = -4 + (some constant value)
-3 = -4 + constant value
constant value = (-3) - (-4)
constant value = 1
Therefore, the rule that represents this function can be expressed as:
y = x + 1
Looking at the answer choices, we can see that option A. y = 1/2x - 1 matches our derived rule, y = x + 1. So, the correct answer is option A.