Is this linear?  X: 0,1,2,3  Y: 4,12,20,28  

To determine whether the relationship between the given \( X \) and \( Y \) values is linear, we need to check if the differences between consecutive \( Y \) values are constant.

Here are the values provided:

- \( X: 0, 1, 2, 3 \)
- \( Y: 4, 12, 20, 28 \)

Let's calculate the differences between consecutive \( Y \) values:

- \( 12 - 4 = 8 \)
- \( 20 - 12 = 8 \)
- \( 28 - 20 = 8 \)

Since the differences between consecutive \( Y \) values are constant (8), the relationship between \( X \) and \( Y \) is linear.

The equation of the line can be found using the slope-intercept form \( Y = mX + b \). The slope \( m \) is the constant difference (8), and when \( X = 0 \), \( Y = 4 \), so the y-intercept \( b = 4 \).

Thus, the equation of the line is:

\[
Y = 8X + 4
\]

This relationship is linear.

Do you want more details or have any questions?

Here are 5 related questions to explore:

1. What is the slope of a non-linear equation?
2. How do you calculate the y-intercept from a given set of points?
3. What would happen if the differences in \( Y \) were not constant?
4. How can you graph the equation \( Y = 8X + 4 \)?
5. What is the geometric interpretation of the slope in a linear equation?

**Tip:** When looking for linearity, always check for constant differences in the dependent variable (Y) for equal intervals in the independent variable (X).

Find out whether the relationship between X: 0,1,2,3 and Y: 4,12,20,28 is linear. Learn how to calculate constant differences, identify the slope, and derive the equation of the line (Y = 8X + 4). Perfect for students in Grades 6-8 exploring linear equations.

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