Answered

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A data set consists of the following data points: (2,4), (4,7), (5,12).

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. 10.5
C. 6
D. 7.5

Sagot :

GinnyAnswer
Let's figure out what the equation of the line of best fit predicts for [tex]\( x = 3 \)[/tex].

The equation of the line of best fit, given in the problem, is:

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

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

1. Start by substituting [tex]\( x = 3 \)[/tex] into the equation:

[tex]\[ y = 2.5 \cdot 3 - 1.5 \][/tex]

2. Next, calculate [tex]\( 2.5 \cdot 3 \)[/tex]:

[tex]\[ 2.5 \cdot 3 = 7.5 \][/tex]

3. Now, subtract 1.5 from 7.5:

[tex]\[ y = 7.5 - 1.5 \][/tex]

4. Performing the subtraction gives:

[tex]\[ y = 6 \][/tex]

Therefore, the equation [tex]\( y = 2.5x - 1.5 \)[/tex] predicts that the value of [tex]\( y \)[/tex] when [tex]\( x = 3 \)[/tex] will be [tex]\( 6 \)[/tex]. Thus, the correct answer is:

C. 6
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