Question

Which equation describes the pattern of the data in the table?

X 3 4 5 6 7
Y 12 16 20 24 28

Answer 1

To find the equation that describes the pattern of the data in the table, we need to analyze the relationship between \( X \) and \( Y \).

Looking at the values given:

\[
\begin{align*}
X: & \quad 3, \quad 4, \quad 5, \quad 6, \quad 7 \\
Y: & \quad 12, \quad 16, \quad 20, \quad 24, \quad 28 \\
\end{align*}
\]

First, we can examine the difference in \( Y \) values as \( X \) increases by 1:

- From \( X = 3 \) to \( X = 4 \): \( 16 - 12 = 4 \)
- From \( X = 4 \) to \( X = 5 \): \( 20 - 16 = 4 \)
- From \( X = 5 \) to \( X = 6 \): \( 24 - 20 = 4 \)
- From \( X = 6 \) to \( X = 7 \): \( 28 - 24 = 4 \)

The changes in \( Y \) are constant, indicating that the relationship is linear.

We can express \( Y \) in terms of \( X \) using the slope-intercept form of a linear equation, which is:

\[
Y = mX + b
\]

Where \( m \) is the slope and \( b \) is the y-intercept.

Since the slope \( m \) is the change in \( Y \) with respect to \( X \), we have:

\[
m = 4
\]

Now, we can find the y-intercept \( b \) by substituting one of the points into the equation \( Y = 4X + b \). Let's use \( (3, 12) \):

\[
12 = 4(3) + b
\]
\[
12 = 12 + b
\]
\[
b = 0
\]

Thus, the linear equation that describes the pattern of the data is:

\[
Y = 4X
\]

So, the equation that describes the pattern of the data is:

\[
Y = 4X
\]