How do I write the equation for this input 0 2 4 6 8 output 21 19 17 15 13?
input plus output = 21
i don't know input/output add25
2 divided by 6+9=
To write the equation for a given input-output relationship, you will need to find the pattern or relationship between the inputs and outputs.
In this case, the output values are decreasing by 2 for every increment of 2 in the input values. Let's break it down step by step:
Input: 0 2 4 6 8
Output: 21 19 17 15 13
We can observe that for each input value, the corresponding output decreases by 2.
So, we can start with the equation y = mx + b, where:
- y represents the output value
- x represents the input value
- m represents the slope (rate of change)
- b represents the y-intercept (the value of y when x is 0)
To determine the slope (m), we can calculate the change in output divided by the change in input:
Slope (m) = (Output2 - Output1) / (Input2 - Input1)
Let's calculate it using the first two pairs of input and output values:
m = (19 - 21) / (2 - 0) = -2 / 2 = -1
Now that we have the slope (m), we can substitute it into the equation:
y = -x + b
To determine the y-intercept (b), we can substitute a known input and output value into the equation and solve for b. We can use any pair of values, but let's use the first pair:
21 = -(0) + b
21 = b
Therefore, b = 21.
Substituting the slope (m) and y-intercept (b) values into the equation, we get:
y = -x + 21
So, the equation for this input-output relationship is y = -x + 21.