Question
Question 6
(Multiple Choice Worth 2 Points)
(Graphing Linear Equations MC)
A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 20 + 10x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
Which graph represents this situation?
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 30 through the point 1 comma 40
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 0 through the point 1 comma 10
Answers
GPT-4o mini
To find the correct graph that represents the equation \( y = 20 + 10x \), we can analyze the components of the equation:
1. **Y-intercept**: The y-intercept is 20, which means when \( x = 0 \) (the gymnast attends 0 classes), the cost is $20 (the monthly fee).
2. **Slope**: The slope is 10, which indicates that for each class attended (each unit increase in \( x \)), the cost increases by $10.
So, the monthly amount paid by the gymnast can be summarized as follows:
- For 0 classes: \( y = 20 + 10(0) = 20 \) (at the point (0, 20))
- For 1 class: \( y = 20 + 10(1) = 30 \) (at the point (1, 30))
- For 2 classes: \( y = 20 + 10(2) = 40 \) (at the point (2, 40))
Based on this information, we can find the correct graph:
- The graph must start at the point (0, 20) and must pass through the point (1, 30).
Among the options provided:
- The correct graph is the one that starts at (0, 20) and goes through (1, 30).
Thus, the answer is:
**Graph with the x-axis labeled "number of classes" and the y-axis labeled "monthly amount in dollars," with a line going from the point (0, 20) through the point (1, 30).**
1. **Y-intercept**: The y-intercept is 20, which means when \( x = 0 \) (the gymnast attends 0 classes), the cost is $20 (the monthly fee).
2. **Slope**: The slope is 10, which indicates that for each class attended (each unit increase in \( x \)), the cost increases by $10.
So, the monthly amount paid by the gymnast can be summarized as follows:
- For 0 classes: \( y = 20 + 10(0) = 20 \) (at the point (0, 20))
- For 1 class: \( y = 20 + 10(1) = 30 \) (at the point (1, 30))
- For 2 classes: \( y = 20 + 10(2) = 40 \) (at the point (2, 40))
Based on this information, we can find the correct graph:
- The graph must start at the point (0, 20) and must pass through the point (1, 30).
Among the options provided:
- The correct graph is the one that starts at (0, 20) and goes through (1, 30).
Thus, the answer is:
**Graph with the x-axis labeled "number of classes" and the y-axis labeled "monthly amount in dollars," with a line going from the point (0, 20) through the point (1, 30).**