Question

Write a function rule for

X

Y

-2

0

-1

2

0

4

1

6

2

8

Answer 1

To find a function rule that describes the relationship between the variables \(X\) and \(Y\) as provided in the table, we can first observe the pairs and look for a pattern.

Here are the provided pairs:

- \(X = -2, Y = 0\)
- \(X = -1, Y = 2\)
- \(X = 0, Y = 4\)
- \(X = 1, Y = 6\)
- \(X = 2, Y = 8\)

Next, we notice the \(Y\) values as \(X\) increases. The changes in \(Y\) can be calculated as follows:

- From \(X = -2\) to \(X = -1\): \(0\) to \(2\) (increases by \(2\))
- From \(X = -1\) to \(X = 0\): \(2\) to \(4\) (increases by \(2\))
- From \(X = 0\) to \(X = 1\): \(4\) to \(6\) (increases by \(2\))
- From \(X = 1\) to \(X = 2\): \(6\) to \(8\) (increases by \(2\))

The differences are consistent, suggesting that \(Y\) changes linearly with \(X\) with a slope of \(2\).

To generate a linear equation in the form \(Y = mX + b\):
- The slope \(m = 2\).
- To find \(b\) (the y-intercept), we can use one of the pairs, for example, \(X = 0\) and \(Y = 4\):
- So, when \(X = 0\), \(Y = b\), which means \(b = 4\).

Now putting these values into the linear equation format:
\[
Y = 2X + 4
\]

Thus, the function rule for the relationship between \(X\) and \(Y\) is:
\[
\boxed{Y = 2X + 4}
\]