Subjects algebra

Distance Points 8C0De8

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1. **State the problem:** We need to find the distance between two points A and B on a number line, where A is at $-2$ and B is at $5$. 2. **Methods to find the distance:** - Method 1: Use the distance formula for points on a number line: $$\text{Distance} = |x_2 - x_1|$$ where $x_1$ and $x_2$ are the coordinates of points A and B. - Method 2: Count the units between the points on the number line directly. 3. **Apply Method 1:** $$\text{Distance} = |5 - (-2)| = |5 + 2| = |7| = 7$$ 4. **Apply Method 2:** Starting at $-2$, count each unit to $5$: from $-2$ to $0$ is $2$ units, and from $0$ to $5$ is $5$ units, total $2 + 5 = 7$ units. 5. **Construct argument for the best method:** The formula method is best because it works for any two points without needing to visualize or count units, especially when points are far apart or not integers. 6. **Generalize strategy:** To find the distance between any two numbers on a number line, use the absolute value of their difference: $$\text{Distance} = |x_2 - x_1|$$ This formula always gives a positive distance regardless of order. **Final answer:** The distance between points A and B is $7$ units.