Please help! I have a test tomorrow. I've been working on this forever and just can't figure out the equation.

Inputs X - 0, 3, 6, 9
Outputs Y - 1, 2, 3, 4

if you divide x by 3 you get

0 1 2 3
add one to that to get
1 2 3 4

so, Y = X/3 + 1

Thanks so much, Mr. Steve!

To figure out the equation that relates the inputs X to the outputs Y, we can approach this problem by looking for a pattern or relationship between the given values.

Looking at the inputs X - 0, 3, 6, 9, and the corresponding outputs Y - 1, 2, 3, 4, we can observe that as X increases by 3 each time, Y increases by 1. This suggests that there is a linear relationship between X and Y.

To confirm this, we can calculate the difference between consecutive inputs and the difference between their corresponding outputs:

For the difference in inputs:
3 - 0 = 3
6 - 3 = 3
9 - 6 = 3

For the difference in outputs:
2 - 1 = 1
3 - 2 = 1
4 - 3 = 1

Both the differences in inputs and outputs are consistent at 3 and 1, respectively, indicating a linear relationship.

Now, to find the equation, we can use the slope-intercept form of a linear equation, which is y = mx + c, where "m" represents the slope and "c" represents the y-intercept.

Since the slope is the rate of change between X and Y, and we have determined that for every increase of 3 in X, there is an increase of 1 in Y, we can set the slope (m) to be 1/3.

Plugging in the values 0 and 1 into the equation y = mx + c, we can determine the y-intercept (c):
1 = (1/3)(0) + c
1 = c

Therefore, the equation that relates X to Y is:
Y = (1/3)X + 1

You can use this equation to determine the output (Y) for any given input (X). For example, if X = 12, you can substitute the value into the equation to find Y:
Y = (1/3)(12) + 1
Y = 4 + 1
Y = 5

By substituting X = 12 into the equation, we find that Y equals 5.