what is rule for a function table that has input/output
12/0
20/2
32/5
52/10
note that output increases by 1 for every input increase of 4,so we're looking for something like
y=x/4
12/4 = 3, so take a look at
y = x/4 - 3
works for me.
To find the rule for this function table, you need to look for patterns between the input (x) and output (y) values. Let's examine the given values:
Input (x) | Output (y)
----------------------
12 | 0
20 | 2
32 | 5
52 | 10
To start, let's consider the relationship between 'x' and 'y' in terms of addition or subtraction. Looking at the table, we can observe that the output values seem to increase as the input values increase.
Now, let's focus on the differences between the 'x' and 'y' values. The differences between consecutive 'x' values in the table are 8, 12, and 20. Similarly, the differences between consecutive 'y' values are 2, 3, and 5.
From this, we can infer that there might be a linear relationship between 'x' and 'y', and the differences between the 'x' and 'y' values represent a constant rate of change.
To calculate the slope/constant rate of change, we can use the formula:
slope = (change in 'y') / (change in 'x')
Using the first two data points:
slope = (2 - 0) / (20 - 12)
= 2 / 8
= 0.25
So, the slope of the equation is 0.25
Now, let's find the equation of the line. We can use the slope-intercept form, y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
Substituting the values of 'm' and one data point (20, 2):
2 = 0.25 * 20 + b
Simplifying the equation:
2 = 5 + b
Subtracting 5 from both sides:
b = -3
Finally, substituting the value of 'b' in the equation, the rule for the function table is:
y = 0.25x - 3.