wht is the function rule that represents the relationship found in the following ordered pairs (-5,22),(10,-23),(4,-5),(-7,28),(6,-11)
To find the function rule that represents the relationship in the given ordered pairs (-5,22), (10,-23), (4,-5), (-7,28), and (6,-11), we need to look for a pattern or a mathematical relationship between the x-values and the corresponding y-values.
Let's start by examining the x-values and y-values separately:
x-values: -5, 10, 4, -7, 6
y-values: 22, -23, -5, 28, -11
By observing the given pairs, we can see that when the x-value increases, the y-value decreases. This suggests a negative relationship.
Next, let's calculate the differences between consecutive x-values and y-values:
Difference in x-values: 10 - (-5) = 15, 4 - 10 = -6, -7 - 4 = -11, 6 - (-7) = 13
Difference in y-values: -23 - 22 = -45, -5 - (-23) = 18, 28 - (-5) = 33, -11 - 28 = -39
Looking at the differences, we can see that the difference in x-values is not constant, whereas the difference in y-values is not constant either.
Since the differences are not constant, we can conclude that the relationship between the x-values and y-values is not linear. It indicates that the function rule is not a simple multiplication or addition of the x-values.
Without a clear pattern or constant relation between the x-values and y-values, we cannot determine a specific function rule based on the given set of ordered pairs.
To find the function rule that represents the relationship in the given ordered pairs, we need to determine the pattern or rule that relates the x-values to the y-values.
Let's look at the x-values first:
- For the ordered pair (-5, 22), x = -5.
- For the ordered pair (10, -23), x = 10.
- For the ordered pair (4, -5), x = 4.
- For the ordered pair (-7, 28), x = -7.
- For the ordered pair (6, -11), x = 6.
Now let's look at the y-values:
- For the ordered pair (-5, 22), y = 22.
- For the ordered pair (10, -23), y = -23.
- For the ordered pair (4, -5), y = -5.
- For the ordered pair (-7, 28), y = 28.
- For the ordered pair (6, -11), y = -11.
To find the function rule, we need to determine how the x-values and y-values are related. Looking at the given ordered pairs, it can be observed that the y-value is obtained by multiplying the x-value by -3 and then subtracting a certain number.
For example:
- For the ordered pair (-5, 22), we can see that 22 = (-5) × (-3) + 7.
- For the ordered pair (10, -23), we can see that -23 = (10) × (-3) + 7.
- For the ordered pair (4, -5), we can see that -5 = (4) × (-3) + 7.
- For the ordered pair (-7, 28), we can see that 28 = (-7) × (-3) + 7.
- For the ordered pair (6, -11), we can see that -11 = (6) × (-3) + 7.
From the above observations, we can find that the function rule that represents the given relationship is:
y = -3x + 7