Question

at a robotics competition, the robotics team can be made of up to 8 people. draw a number line to represent the number of people that could be on a team. any value less than or equal to 8 p ≤ 8

Explanation:

Step1: Understand the inequality

The number of people \( p \) on the team satisfies \( p \leq 8 \). This means \( p \) can be any integer from \( 0 \) (or \( 1 \), depending on context, but since it's a team, at least \( 1 \)) up to \( 8 \), and also includes all real numbers in that range if we consider non - integer values (though in this context, it's likely integer, but the number line representation for \( p\leq8 \) is general).

Step2: Draw the number line

1. First, identify the point \( 8 \) on the number line.
2. Since the inequality is \( \leq \), we use a closed circle (filled circle) at \( 8 \) to indicate that \( 8 \) is included in the solution set.
3. Then, we draw an arrow starting from the closed circle at \( 8 \) and pointing to the left (towards negative infinity or towards smaller numbers) to represent all numbers less than or equal to \( 8 \).

Looking at the given number line, we should have a closed circle at \( 8 \) (since \( p = 8 \) is allowed, as the team can be made up of up to \( 8 \) people, meaning \( 8 \) is included) and the arrow pointing to the left (towards \( 1,2,\cdots,7 \) and beyond towards smaller numbers).

Answer:

To represent \( p\leq8 \) on the number line:

• Place a closed (filled) circle at \( 8 \) (because \( 8 \) is included in the set of possible number of people, as the team can have up to \( 8 \) people).
• Draw an arrow starting from the closed circle at \( 8 \) and extending to the left (towards smaller numbers like \( 7,6,5,\cdots \)) to show all values of \( p \) that are less than or equal to \( 8 \).