Lorrie is playing a board game. She started her playing piece five spaces from the starting circle. During the remainder of the game, she advanced only one space per turn. Which of the following shows how the number of spaces, y, changes as the turn, x, changes

Question

A graph titled board game compares number of spaces versus turn. A straight line extends between (0, 5) and (5, 10). The values are approximate.
W.	A graph titled board game compares number of spaces versus turn. A straight line extends between (3, 0) and (10, 7). The values are approximate.
X.
A graph titled board game compares number of spaces versus turn. A straight line extends between (5, 0) and (10, 5). The values are approximate.
Y.	A graph titled board game compares number of spaces versus turn. A straight line extends between (0, 0) and (10, 10). The values are approximate.
Z.
 A. 
Y
 B. 
Z
 C. 
W
 D. 
X

GPT-4o mini · Answer

To determine which graph represents Lorrie's progress in the game, we need to analyze how her position changes with each turn:

Lorrie starts 5 spaces away from the starting circle.
She advances 1 space per turn.

This means that after \( x \) turns, her position (the number of spaces from the starting point, \( y \)) can be described by the equation:

\[ y = 5 + x \]

This means that:

When \( x = 0 \), \( y = 5 \).
When \( x = 1 \), \( y = 6 \).
When \( x = 2 \), \( y = 7 \).
When \( x = 3 \), \( y = 8 \).
When \( x = 4 \), \( y = 9 \).
When \( x = 5 \), \( y = 10 \).

From this, we can see that \( y \) increases linearly as \( x \) increases. The graph must start at (0, 5) and will continue to rise as \( x \) increases.

Now, let's analyze the options given:

A: (0, 5) to (5, 10) indicates an increase from \( y = 5 \) to \( y = 10 \) as \( x \) increases from 0 to 5. This fits Lorrie's movements well.
B: Does not start from (0, 5) and does not fit the movement.
C: Does not start from (0, 5) and resembles a different movement.
D: Starts from (0, 0) and doesn't match Lorrie's start position.

Thus, the graph that accurately represents Lorrie's progression in the game is option A.

Answer: A.