Question
Meg bought a season pass at Elk Mountain Ski Resort to access the ski slopes, and she plans to rent her equipment from the resort each day she skis. The total amount Meg will pay by the end of the season depends on how many days she skis.
This situation can be modeled as a linear relationship.
What does the y-intercept of the line tell you about the situation? (-2,-10)
This situation can be modeled as a linear relationship.
What does the y-intercept of the line tell you about the situation? (-2,-10)
Answers
GPT-4o mini
In the context of Meg's situation with the season pass at Elk Mountain Ski Resort, the y-intercept of the linear relationship represents the initial cost associated with her skiing, independent of how many days she actually skis.
For the coordinates (-2, -10), we can interpret the point as follows:
- The x-coordinate (-2) does not have a direct physical meaning in this case because it likely represents a hypothetical scenario where Meg skis a negative number of days, which is not possible in a real-world context.
- The y-coordinate (-10) suggests that if Meg were to ski a number of days that corresponds to -2, she would incur a cost of -10.
While we can't directly use this point for interpretation in a practical sense, it highlights that the line potentially represents her expenses in a way that reflects a model, but skiing negative days doesn't apply here.
A more relevant interpretation of the y-intercept in a typical scenario would usually be considered when the x-value is zero (0), where it represents the cost that Meg incurs simply by purchasing the season pass without any extra costs from rentals.
Thus, while (-2, -10) isn't applicable in a real situation, if we were analyzing a point where x = 0 (like her expenses when she has not skied at all), the y-intercept would give us insight into the fixed costs associated with her skiing pass, such as the cost of the pass itself without any rentals.
For the coordinates (-2, -10), we can interpret the point as follows:
- The x-coordinate (-2) does not have a direct physical meaning in this case because it likely represents a hypothetical scenario where Meg skis a negative number of days, which is not possible in a real-world context.
- The y-coordinate (-10) suggests that if Meg were to ski a number of days that corresponds to -2, she would incur a cost of -10.
While we can't directly use this point for interpretation in a practical sense, it highlights that the line potentially represents her expenses in a way that reflects a model, but skiing negative days doesn't apply here.
A more relevant interpretation of the y-intercept in a typical scenario would usually be considered when the x-value is zero (0), where it represents the cost that Meg incurs simply by purchasing the season pass without any extra costs from rentals.
Thus, while (-2, -10) isn't applicable in a real situation, if we were analyzing a point where x = 0 (like her expenses when she has not skied at all), the y-intercept would give us insight into the fixed costs associated with her skiing pass, such as the cost of the pass itself without any rentals.