Questions: The scatter plot shows the time spent studying, (x), and the quiz score, (y), for each of 25 students. Use the scatter plot to answer the parts below. (Note that you can use the graphing tools to help you approximate the line.) (a) Write an approximate equation of the line of best fit. Round the coefficients to the nearest hundredth. (b) Using your equation from part (a), predict the quiz score for a student who spent 70 minutes studying. Round your prediction to the nearest hundredth.

The scatter plot shows the time spent studying, (x), and the quiz score, (y), for each of 25 students. Use the scatter plot to answer the parts below. (Note that you can use the graphing tools to help you approximate the line.) (a) Write an approximate equation of the line of best fit. Round the coefficients to the nearest hundredth. (b) Using your equation from part (a), predict the quiz score for a student who spent 70 minutes studying. Round your prediction to the nearest hundredth.
Transcript text: The scatter plot shows the time spent studying, $x$, and the quiz score, $y$, for each of 25 students. Use the scatter plot to answer the parts below. (Note that you can use the graphing tools to help you approximate the line.) Scratch Area (Not Part of Answer) (a) Write an approximate equation of the line of best fit. Round the coefficients to the nearest hundredth. \[ y= \] $\square$ (b) Using your equation from part (a), predict the quiz score for a student who spent 70 minutes studying. Round your prediction to the nearest hundredth. $\square$
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Solution

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Solution Steps

Step 1: Identify the points on the scatter plot
  • Observe the scatter plot and identify the general trend of the points.
  • The points show a positive correlation between time spent studying (x) and quiz score (y).
Step 2: Determine the line of best fit
  • Use the scatter plot to approximate the line of best fit.
  • Select two points that lie close to the line of best fit. For example, (10, 30) and (80, 90).
Step 3: Calculate the slope (m) of the line
  • Use the formula for the slope: \( m = \frac{y_2 - y_1}{x_2 - x_1} \)
  • For points (10, 30) and (80, 90): \[ m = \frac{90 - 30}{80 - 10} = \frac{60}{70} \approx 0.86 \]
Step 4: Determine the y-intercept (b)
  • Use the slope-intercept form \( y = mx + b \) and one of the points to solve for b.
  • Using point (10, 30): \[ 30 = 0.86 \cdot 10 + b \implies 30 = 8.6 + b \implies b = 30 - 8.6 = 21.4 \]
Step 5: Write the equation of the line of best fit
  • Combine the slope and y-intercept to form the equation: \[ y = 0.86x + 21.4 \]
Step 6: Predict the quiz score for 70 minutes of studying
  • Substitute \( x = 70 \) into the equation: \[ y = 0.86 \cdot 70 + 21.4 = 60.2 + 21.4 = 81.6 \]

Final Answer

  • The equation of the line of best fit is \( y = 0.86x + 21.4 \).
  • The predicted quiz score for a student who spent 70 minutes studying is 81.6.
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