FIND THE FUNCTION RULE
x: -2, -1, 0, 1 , 2
y: 9 , 4, -1, -6, -11
looks like for every increase of 1 in the x, our y decreases by 5
so it must be
y = -5x + c
all we need is to find c
pick one of the data values:
0 = 0, y = -1
-1 = 0 + c
c = -1
y = -5x - 1
thx
C means x!!!!!!!!
what is c mean?????
what does "c" mean?
Oh, I love playing the role of a detective! Let's solve this mystery!
Looking at the relationship between x and y, we can see a pattern. It seems that for every increase of 1 in x, y decreases by 5. So, we can conclude that the function rule is:
y = -5x + something
To find out what that "something" is, let's take a closer look. When x is 0, y is -1. So, substituting those values into our function rule, we get:
-1 = -5(0) + something
Since anything multiplied by zero is zero, we find that:
-1 = something
Therefore, the function rule is:
y = -5x - 1
Now you have the answer! Solve away, my detective friend!
To find the function rule, we can look for a pattern in the given input-output pairs.
Let's observe the relationship between the x-values and the corresponding y-values:
- When x = -2, y = 9
- When x = -1, y = 4
- When x = 0, y = -1
- When x = 1, y = -6
- When x = 2, y = -11
From the given data, we can see that the y-values are decreasing by 5 for each successive x-value. This suggests that there is a constant rate of change of -5.
Now, let's try to express this relationship in terms of a function. We can start by guessing that the function might be linear, in the form of y = mx + b, where m represents the slope (rate of change) and b represents the y-intercept.
Using the first data point (x = -2, y = 9), we can substitute these values into the equation:
9 = -2m + b
Similarly, using the second data point (x = -1, y = 4):
4 = -1m + b
Now, we have a system of two equations:
-2m + b = 9 -- Equation 1
-m + b = 4 -- Equation 2
We can solve this system of equations simultaneously to find the values of m and b, which will help us determine the function rule.
Adding Equation 1 and Equation 2, we get:
-3m + 2b = 13 -- Equation 3
Subtracting Equation 2 from Equation 1, we get:
-3m = 5
Simplifying the equation further, we find:
m = -5/3
Substituting the value of m into Equation 2, we have:
(-5/3) + b = 4
Solving for b, we find:
b = 4 + 5/3
b = (12 + 5) / 3
b = 17/3
So, the function rule that describes the relationship between x and y is:
y = (-5/3)x + 17/3