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A data set consists of the following data points:
[tex](2,4), (4,7), (5,12)[/tex]

The line of best fit has the equation [tex]y = 2.5x - 1.5[/tex]. What does this equation predict for a value of [tex]x = 3[/tex]?

A. 9
B. 6
C. 7.5
D. 10.5



Answer :

GinnyAnswer
To solve the problem, we start with the given equation of the line of best fit:

[tex]\[ y = 2.5x - 1.5 \][/tex]

We need to predict the value of [tex]\( y \)[/tex] when [tex]\( x = 3 \)[/tex].

Step-by-step:

1. Substitute [tex]\( x = 3 \)[/tex] into the equation:
[tex]\[ y = 2.5(3) - 1.5 \][/tex]

2. Calculate [tex]\( 2.5 \times 3 \)[/tex]:
[tex]\[ 2.5 \times 3 = 7.5 \][/tex]

3. Subtract 1.5 from 7.5:
[tex]\[ y = 7.5 - 1.5 \][/tex]
[tex]\[ y = 6 \][/tex]

Thus, the predicted value of [tex]\( y \)[/tex] when [tex]\( x = 3 \)[/tex] is [tex]\( 6 \)[/tex].

Therefore, the correct answer is:
[tex]\[ \boxed{6} \][/tex]

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