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On a graph titled Time Spent and Test Grades, a line and ten points are plotted in quadrant 1 of a coordinate plane. The x-axis is labeled Hours Worked, and the y-axis is labeled Grade.

The data in the graph represents the relationship between the amount of time spent studying and test grades. Each point represents a piece of data collected from students who took a test and the grade that student received. For example, (2,70)
represents a student who studied for 2 hours and received a 70. Decide which model best fits this data.

(1 point)
Responses

a quadratic model
a quadratic model

no model
no model

a linear model
a linear model

an exponential model
an exponential model
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1 answer

To determine which model best fits the data represented in the graph titled "Time Spent and Test Grades," we should consider the nature of the relationship between the two variables: Hours Worked (x-axis) and Grade (y-axis).

  1. Linear Model: If the points on the graph generally form a straight line, this would indicate a linear relationship, suggesting that as study hours increase, grades increase at a constant rate.

  2. Quadratic Model: If the points on the graph create a parabolic shape (either opening upwards or downwards), this would suggest a quadratic relationship, indicating that the relationship might involve a variable rate of change.

  3. Exponential Model: If the points show a rapidly increasing pattern, where a small increase in study hours leads to a large increase in grades, this could point to an exponential relationship.

  4. No Model: If the points are scattered without a discernible pattern, then no model would fit the data.

Since I can't see the graph, if you describe the pattern of the data points you observe (whether they appear in a straight line, curve, or scattered), I can help you better determine which model might fit the data best. However, based on typical educational trends, if the relationship appears generally positive and linear (more study hours typically lead to higher grades), a linear model might be the best fit. If there’s significant variability, you might consider the other options.