Write an equation involving absolute value for the graph -2 and 4

To create an equation involving absolute values for the points \(-2\) and \(4\), we can use the midpoint of these two numbers to create an absolute value equation that expresses the distance between any point \(x\) and the midpoint of the two points. The midpoint between \(-2\) and \(4\) is:

\[
\text{Midpoint} = \frac{-2 + 4}{2} = 1
\]

The absolute value equation expressing the distance between \(x\) and the midpoint 1, while covering both points \(-2\) and \(4\), is:

\[
|x - 1| = 3
\]

This equation means that the distance between \(x\) and \(1\) is always 3 units, which places \(x\) at \(-2\) or \(4\). Therefore, this absolute value equation represents the points \(-2\) and \(4\) on a number line.

Would you like more details or have any questions?

Here are five related questions for further exploration:
1. How would the equation change if the points were \(-5\) and \(3\)?
2. What would the absolute value equation look like if the graph had only one point, such as \(2\)?
3. How can you graph this equation on a coordinate plane?
4. What is the general formula for an absolute value equation given two points on a number line?
5. How can this absolute value equation be solved algebraically?

**Tip:** When dealing with absolute value equations, think of them as representing distances from a certain point.

Write an equation involving absolute value for the graph -2 and 4.

Discover how to write an absolute value equation for the points -2 and 4 on a number line. This problem involves finding the midpoint between the two points and expressing the distance using an absolute value equation. Suitable for middle school students learning about algebra and absolute value.

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