Question

clare said the distance between points a and b on a number line can be found using the expression | -7 - 3| which number line can be the one clare used? a. number line with b at -7, a at 3 b. number line with b at 3, a at 7 c. number line with b at -7, a at -3 d. number line with b at -4, a at 3

Explanation:

Step1: Analyze the expression

The distance formula between two points \( x_1 \) and \( x_2 \) on a number line is \( |x_1 - x_2| \) (or \( |x_2 - x_1| \)). Here, the expression is \( | - 7-3| \), which means one point is \( - 7 \) (let's say \( b=-7 \)) and the other is \( 3 \) (let's say \( a = 3 \)).

Step2: Check each option

• Option A: \( b=-7 \), \( a = 3 \). This matches the values we inferred from the expression \( |-7 - 3| \) (since \( b=-7 \) and \( a = 3 \), the distance is \( |-7 - 3| \)).
• Option B: \( b = 3 \), \( a=7 \). The distance would be \( |3 - 7|=|-4| = 4\), not \( |-7 - 3|=10 \).
• Option C: \( b=-7 \), \( a=-3 \). The distance would be \( |-7-(-3)|=|-4| = 4\), not \( 10 \).
• Option D: \( b=-4 \), \( a = 3 \). The distance would be \( |-4 - 3|=|-7| = 7\), not \( 10 \).

Answer:

A. The number line with \( b \) at -7 and \( a \) at 3 (as shown in option A's graph)