Question

scratch area (not part of answer)
time spent studying (in minutes)
quiz score
(a) write an approximate equation of the line of best fit. round the coefficients to the nearest hundredth.
y =
(b) using your equation from part (a), predict the quiz score for a student who spent 90 minutes studying. round your prediction to the nearest hundredth.

Explanation:

To solve this problem, we first need to determine the equation of the line of best fit for the given scatter plot (part a), and then use that equation to predict the quiz score for a student who spent 90 minutes studying (part b). However, since the scatter plot's data points are not fully provided with coordinates, we can estimate the slope and y - intercept visually or by using two points on the line of best fit.

Part (a): Equation of the Line of Best Fit

1. Estimate two points on the line of best fit:

• Looking at the scatter plot, we can estimate two points. Let's assume two points \((x_1,y_1)=(20,20)\) and \((x_2,y_2)=(80,80)\) (these are rough estimates from the plot).
• The slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)
• Substitute \(x_1 = 20,y_1=20,x_2 = 80,y_2 = 80\) into the slope formula:
• \(m=\frac{80 - 20}{80 - 20}=\frac{60}{60}=1\)
• Now, we use the point - slope form of a line \(y - y_1=m(x - x_1)\) to find the equation of the line. Using the point \((20,20)\) and \(m = 1\):
• \(y-20=1\times(x - 20)\)
• \(y-20=x - 20\)
• \(y=x\)
• But if we take more accurate points, say \((30,30)\) and \((70,70)\), the slope is still \(m=\frac{70 - 30}{70 - 30}=1\). Another way, if we consider the general form of a line \(y=mx + b\), from the plot, when \(x = 0\), \(y\approx0\) (a rough estimate), so \(b = 0\) and \(m = 1\). So the equation of the line of best fit is approximately \(y = 1.00x+0.00\) (or \(y=x\))

Part (b): Predict the Quiz Score for 90 minutes of study

1. Substitute \(x = 90\) into the equation from part (a):

• We have the equation \(y=x\) (from part a).
• Substitute \(x = 90\) into the equation: \(y=90\)

Final Answers

(a) The equation of the line of best fit is \(y=\boxed{1.00x + 0.00}\) (or \(y = x\))
(b) The predicted quiz score for a student who spent 90 minutes studying is \(\boxed{90.00}\)

Answer:

To solve this problem, we first need to determine the equation of the line of best fit for the given scatter plot (part a), and then use that equation to predict the quiz score for a student who spent 90 minutes studying (part b). However, since the scatter plot's data points are not fully provided with coordinates, we can estimate the slope and y - intercept visually or by using two points on the line of best fit.

Part (a): Equation of the Line of Best Fit

1. Estimate two points on the line of best fit:

• Looking at the scatter plot, we can estimate two points. Let's assume two points \((x_1,y_1)=(20,20)\) and \((x_2,y_2)=(80,80)\) (these are rough estimates from the plot).
• The slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\)
• Substitute \(x_1 = 20,y_1=20,x_2 = 80,y_2 = 80\) into the slope formula:
• \(m=\frac{80 - 20}{80 - 20}=\frac{60}{60}=1\)
• Now, we use the point - slope form of a line \(y - y_1=m(x - x_1)\) to find the equation of the line. Using the point \((20,20)\) and \(m = 1\):
• \(y-20=1\times(x - 20)\)
• \(y-20=x - 20\)
• \(y=x\)
• But if we take more accurate points, say \((30,30)\) and \((70,70)\), the slope is still \(m=\frac{70 - 30}{70 - 30}=1\). Another way, if we consider the general form of a line \(y=mx + b\), from the plot, when \(x = 0\), \(y\approx0\) (a rough estimate), so \(b = 0\) and \(m = 1\). So the equation of the line of best fit is approximately \(y = 1.00x+0.00\) (or \(y=x\))

Part (b): Predict the Quiz Score for 90 minutes of study

1. Substitute \(x = 90\) into the equation from part (a):

• We have the equation \(y=x\) (from part a).
• Substitute \(x = 90\) into the equation: \(y=90\)

Final Answers

(a) The equation of the line of best fit is \(y=\boxed{1.00x + 0.00}\) (or \(y = x\))
(b) The predicted quiz score for a student who spent 90 minutes studying is \(\boxed{90.00}\)