https://file.aiquickdraw.com/mathbot/file/1727313371606bl0wk0q2.jpg

The problem states that a car moves from \( x_1 = 20 \, \text{mi} \) to \( x_2 = 62 \, \text{mi} \), and you are asked to:

1. **Draw a picture with the coordinate axis**, marking the zero point, \( x_1 \), and \( x_2 \).
2. **Find \( \Delta x \)**, which represents the change in position.

Let's break it down:

### Step 1: Drawing the Coordinate Axis
The coordinate axis would be a horizontal number line where the zero point (0) is marked, along with the two positions:

- \( x_1 = 20 \, \text{mi} \) (starting position)
- \( x_2 = 62 \, \text{mi} \) (final position)

You would place 0 as the origin, then mark 20 on the number line for \( x_1 \) and 62 for \( x_2 \), both to the right of the origin since they are positive values.

### Step 2: Finding \( \Delta x \)
The change in position \( \Delta x \) is given by:
\[
\Delta x = x_2 - x_1
\]
Substituting the given values:
\[
\Delta x = 62 \, \text{mi} - 20 \, \text{mi} = 42 \, \text{mi}
\]

### Final Answer:
- **Coordinate Axis**: Mark 0, 20, and 62 on a number line.
- **Change in Position** \( \Delta x \): \( 42 \, \text{mi} \)

Would you like me to generate a visual image of the coordinate axis, or do you need further clarifications on the solution?

### Related Questions:
1. What is the physical significance of \( \Delta x \) in real-world motion?
2. How would the coordinate axis change if the car started at \( x_1 = -20 \, \text{mi} \)?
3. How do we compute \( \Delta x \) if the final position is less than the initial one?
4. What additional information would you need to compute the average speed of the car?
5. How can the concept of \( \Delta x \) apply to displacement in two-dimensional motion?

### Tip:
Always remember that \( \Delta x \) represents a scalar quantity and refers only to the change in position along a straight line, not the direction of travel.

A car moved from x₁ = 20 mi to x₂ = 62 mi. Draw a picture with the coordinate axis, zero point, and the locations x₁ and x₂, and find Δx.

Learn how to find the change in position (Δx) when a car moves from x₁ = 20 mi to x₂ = 62 mi. The problem involves drawing a coordinate axis and calculating the displacement using Δx = x₂ - x₁. Ideal for Grades 6-8.

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