To analyze Tanica's prediction using the line of best fit, we start with the given equation of the line:
\[ y \approx -1.02x + 7.09 \]
Now, we need to substitute \( x = 0.5 \) into this equation to find the corresponding value of \( y \):
\[ y \approx -1.02(0.5) + 7.09 \] \[ y \approx -0.51 + 7.09 \] \[ y \approx 6.58 \]
Tanica predicted that when \( x = 0.5 \), \( y \) would be approximately \( 7.6 \). However, the calculation shows that the actual value of \( y \) is approximately \( 6.58 \).
The options provided for her mistake are:
- She drew the line of best fit incorrectly.
- She used the line of best fit to predict \( y \) for an incorrect value of \( x \).
- She forgot the minus sign before the first term on the right side of the equation when she predicted \( y \).
- She plugged \( 0.5 \) into the equation for \( y \) instead of \( x \) and actually predicted \( x \) instead of \( y \).
Tanica's prediction was incorrect, and it appears she wrongly calculated \( y \) when \( x = 0.5 \). Therefore, she made a mistake by not performing the calculation correctly with the correct value of \( x \).
The most accurate conclusion is that:
She forgot the minus sign before the first term on the right side of the equation when she predicted \( y \).
This is consistent with her prediction being too high since a negative coefficient in the equation would lower the value of \( y \). Therefore, option 3 is likely the best choice to explain her mistake.
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