Find the function rule
X= -2,-1,0,1,2
Y= 9,4,-1,-6,-11
I don't want the answer I just want to know how to do it
Does anyone know
Is there anyone who can help me?
the term- to-term difference in the x values is 1
the term- to-term difference in the y values is -5
y = -5 x + b
plug in a pair of values to find b
To find the function rule, you need to observe the relationship between the given input values (X) and the corresponding output values (Y).
In this case, the given X values are -2, -1, 0, 1, 2, and the corresponding Y values are 9, 4, -1, -6, -11.
To determine the function rule, analyze how the Y values are changing as the X values change. Look for patterns or trends in the data.
One approach is to identify the difference between consecutive pairs of Y values and compare them to the difference between corresponding X values. If the differences are consistent, it indicates that the function is linear.
Let's find the differences between consecutive Y values:
4 - 9 = -5
-1 - 4 = -5
-6 - (-1) = -5
-11 - (-6) = -5
All the differences are the same (-5).
Now, let's find the differences between consecutive X values:
-1 - (-2) = 1
0 - (-1) = 1
1 - 0 = 1
2 - 1 = 1
The differences between the X values are also consistent (1).
Based on these observations, we can conclude that the function rule is a linear function.
To find the exact rule, you can use the formula for the linear function: Y = MX + B, where M is the slope and B is the y-intercept.
To calculate the slope (M), choose any two points from the given data. Let's use the points (-2, 9) and (2, -11):
M = (Y2 - Y1) / (X2 - X1)
= (-11 - 9) / (2 - (-2))
= (-20) / 4
= -5
Now, substitute the slope value (-5) and one of the points (-2, 9) into the formula to find the y-intercept (B):
9 = (-5)(-2) + B
Simplify the equation:
9 = 10 + B
Now, isolate B:
B = 9 - 10
B = -1
Therefore, the function rule for the given X and Y values is: Y = -5X - 1.