I need help for the rule for input 1/output 3, input 3/output 17, input 10/output 66, and input 6/output 38
x y
1 3
3 17
6 38
10 66
check the slope between each two points:
(17-3)/(3-1) = 14/2 = 7
(38-17)/(6-3) = 21/3 = 7
(66-38)/(10-6) = 28/4 = 7
Clearly the points lie on a line with slope 7.
Since 7*1 = 7, but y(1) = 3, the rule must be
y = 7x-4
To find the rule for the given inputs and outputs, we need to look for a pattern or relationship between them. Let's examine the differences between the input numbers and the output numbers:
For input 1:
Output = 3
Difference = Output - Input = 3 - 1 = 2
For input 3:
Output = 17
Difference = Output - Input = 17 - 3 = 14
For input 10:
Output = 66
Difference = Output - Input = 66 - 10 = 56
For input 6:
Output = 38
Difference = Output - Input = 38 - 6 = 32
Observing the differences between the inputs and outputs, we can notice that the differences increase by 12 each time: 2, 14, 56, 32.
If we continue the sequence of differences, we would have: 2, 14, 56, 32, 44, 56, 68, ...
Based on this pattern, we can assume that the rule for finding the output is to multiply the input by 12 and then subtract 10. This can be represented as:
Output = (Input x 12) - 10
Let's verify if this rule holds true for the given inputs:
For input 1:
Output = (1 x 12) - 10 = 2
For input 3:
Output = (3 x 12) - 10 = 16
For input 10:
Output = (10 x 12) - 10 = 110
For input 6:
Output = (6 x 12) - 10 = 62
According to this rule, the output values are 2, 16, 110, and 62 for the given inputs of 1, 3, 10, and 6, respectively.