Please help me find the rule input 0 output 2 then input 1 output 4 next input 2 output 6 then input 3 output 8 last input 4 output 10
Thanks
If you suspect that the rule is a straight line,
y=mx+b
then find the slope using
m=(y2-y1)/(x2-x1)
Substitute m and (x1,y1) into the equation to find b.
Verify that the rule applies to all the points.
First make a table to show input and output.
IN. OUT
0. 2
1. 4
2. 6
.. ..
Notice that the difference between outputs is 2.
But 2 times each input does NOT give the correct output. However, if you add 2 to the product of 2 and input, you get the correct output.
Therefore, the rule is 2x +2 where x is the input.
To find the rule for the given inputs and outputs, we need to observe the pattern in the outputs and try to identify a mathematical relationship between the inputs and outputs. Let's analyze the given information:
Input 0 -> Output 2
Input 1 -> Output 4
Input 2 -> Output 6
Input 3 -> Output 8
Input 4 -> Output 10
Looking at the outputs, we notice that each output value is 2 more than double the input value. To express this relationship mathematically, we can use the formula:
Output = (2 * Input) + 2
Applying this formula to each given input, we can verify if it holds true:
For Input 0:
Output = (2 * 0) + 2
Output = 0 + 2
Output = 2 (Matches the given output)
For Input 1:
Output = (2 * 1) + 2
Output = 2 + 2
Output = 4 (Matches the given output)
For Input 2:
Output = (2 * 2) + 2
Output = 4 + 2
Output = 6 (Matches the given output)
For Input 3:
Output = (2 * 3) + 2
Output = 6 + 2
Output = 8 (Matches the given output)
For Input 4:
Output = (2 * 4) + 2
Output = 8 + 2
Output = 10 (Matches the given output)
Since the formula (Output = (2 * Input) + 2) holds true for all the given inputs and outputs, we can conclude that it represents the rule or pattern in this sequence.