Looking at the graph, answer the following questions:

Question

(3 points)
1) Write an equation for the line of best fit
y = 6x + 55

2) Make a prediction for a student who studies 6 hours on what their math grade will be
90%

3) Make a prediction of how many hours a student would need to study for a grade of 40%
0

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Answer 1

Sure! Based on the information provided:

1. The equation for the line of best fit is given as: \[ y = 6x + 55 \]

2. To predict the math grade for a student who studies for 6 hours, substitute \(x = 6\) into the equation: \[ y = 6(6) + 55 = 36 + 55 = 91 \] Therefore, the predicted math grade for a student who studies 6 hours is 91%.

3. To find out how many hours a student would need to study for a grade of 40%, set \(y = 40\) and solve for \(x\): \[ 40 = 6x + 55 \] Rearranging the equation gives: \[ 6x = 40 - 55 \] \[ 6x = -15 \] \[ x = -\frac{15}{6} = -2.5 \] This suggests that in order to achieve a grade of 40%, a student would need to study for \(-2.5\) hours, which is not feasible—in practical terms, this implies that it's impossible to achieve a 40% grade based on the data provided.

If you have any more questions or need further clarification, feel free to ask!