Answered

Discover a world of knowledge at Westonci.ca, where experts and enthusiasts come together to answer your questions. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.