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What is the equation of the line of best fit for the following data? Round the slope and [tex]y[/tex]-intercept of the line to three decimal places.

\begin{tabular}{|c|c|}
\hline [tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline 1 & 14 \\
\hline 5 & 11 \\
\hline 6 & 4 \\
\hline 12 & 2 \\
\hline 15 & 1 \\
\hline
\end{tabular}

A. [tex]y=0.927x-13.634[/tex]
B. [tex]y=13.634x-0.927[/tex]
C. [tex]y=-0.927x+13.634[/tex]
D. [tex]y=-13.634x+0.927[/tex]

Sagot :

GinnyAnswer
To find the equation of the line of best fit for the given data, we start with the pairs of points: [tex]\((1, 14)\)[/tex], [tex]\((5, 11)\)[/tex], [tex]\((6, 4)\)[/tex], [tex]\((12, 2)\)[/tex], and [tex]\((15, 1)\)[/tex].

The equation of a line in slope-intercept form is:
[tex]\[ y = mx + b \][/tex]
where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.

The given result presents the slope [tex]\( m \)[/tex] and the y-intercept [tex]\( b \)[/tex] for the line of best fit, rounded to three decimal places:

Slope: [tex]\( m = -0.927 \)[/tex]
Y-intercept: [tex]\( b = 13.634 \)[/tex]

Therefore, the equation of the line of best fit is:
[tex]\[ y = -0.927x + 13.634 \][/tex]

So the correct answer is:

C. [tex]\( y = -0.927x + 13.634 \)[/tex]
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