Question
Sam has $50.00 to spend this month on his cell phone plan. Calls cost $0.10 per minute, and text messages cost $0.05 per message.
Which of the following graphs represents this situation?
J.
K.
L.
Which of the following graphs represents this situation?
J.
K.
L.
Answers
GPT-4o mini
To represent Sam's cell phone plan budget graphically, we first need to create an equation based on the costs of calls and text messages.
Let:
- \( x \) = number of minutes of calls
- \( y \) = number of text messages
Given:
- Cost per minute for calls = $0.10
- Cost per message for texts = $0.05
- Total budget = $50.00
The total cost for calls and texts can be represented as:
\[ 0.10x + 0.05y = 50 \]
To make this equation easier to work with, we can multiply the entire equation by 100 to eliminate the decimals:
\[ 10x + 5y = 5000 \]
This can be simplified to:
\[ 2x + y = 1000 \]
The equation \( y = -2x + 1000 \) indicates a linear relationship where:
- The y-intercept (when \( x = 0 \)) is 1000 messages.
- The x-intercept (when \( y = 0 \)) is 500 minutes of calls.
The graph would be a straight line with a negative slope, starting from the y-intercept and crossing the x-axis.
To determine which graph corresponds to this equation, look for:
1. A linear graph that ranges from a high number of text messages (close to 1000) when no minutes are used (when \( x = 0 \)).
2. It shows a downward slope where the number of messages decreases as the number of minutes increases.
Since I can't see the graphs (J, K, or L), you'll need to compare those graphs to find one that has these characteristics: a negatively sloped line with intercepts at approximately (0, 1000) and (500, 0). Look for the line that accurately depicts this relationship.
Let:
- \( x \) = number of minutes of calls
- \( y \) = number of text messages
Given:
- Cost per minute for calls = $0.10
- Cost per message for texts = $0.05
- Total budget = $50.00
The total cost for calls and texts can be represented as:
\[ 0.10x + 0.05y = 50 \]
To make this equation easier to work with, we can multiply the entire equation by 100 to eliminate the decimals:
\[ 10x + 5y = 5000 \]
This can be simplified to:
\[ 2x + y = 1000 \]
The equation \( y = -2x + 1000 \) indicates a linear relationship where:
- The y-intercept (when \( x = 0 \)) is 1000 messages.
- The x-intercept (when \( y = 0 \)) is 500 minutes of calls.
The graph would be a straight line with a negative slope, starting from the y-intercept and crossing the x-axis.
To determine which graph corresponds to this equation, look for:
1. A linear graph that ranges from a high number of text messages (close to 1000) when no minutes are used (when \( x = 0 \)).
2. It shows a downward slope where the number of messages decreases as the number of minutes increases.
Since I can't see the graphs (J, K, or L), you'll need to compare those graphs to find one that has these characteristics: a negatively sloped line with intercepts at approximately (0, 1000) and (500, 0). Look for the line that accurately depicts this relationship.