Question

the table shows the number of times different documents were reviewed and the total number of errors that were found on each document. document review
which equation best represents the line - of - best fit for the data in the table?
$y=-2x + 12$
$y=-\frac{3}{2}x + 8$
$y=-\frac{5}{3}x + 10$
$y=-3x + 14$

Explanation:

Step1: Calculate the mean of \(x\) and \(y\)

First, find the sum of \(x\) values: \(5 + 4+2 + 2+1 + 4+3 + 3=24\). There are \(n = 8\) data points. So, \(\bar{x}=\frac{24}{8}=3\).
Next, find the sum of \(y\) values: \(2 + 2+6 + 8+8 + 4+4 + 6=40\). Then, \(\bar{y}=\frac{40}{8}=5\).

Step2: Check each equation with \((\bar{x},\bar{y})\)

• For \(y=-2x + 12\), when \(x = 3\), \(y=-2\times3+12=6

eq5\).

• For \(y=-\frac{3}{2}x + 8\), when \(x = 3\), \(y=-\frac{3}{2}\times3 + 8=-\frac{9}{2}+8=\frac{-9 + 16}{2}=\frac{7}{2}=3.5

eq5\).

• For \(y=-\frac{5}{3}x + 10\), when \(x = 3\), \(y=-\frac{5}{3}\times3+10=-5 + 10=5\).
• For \(y=-3x + 14\), when \(x = 3\), \(y=-3\times3+14=-9 + 14=5\).

Step3: Check another data point

Take the point \((x = 5,y = 2)\)

• For \(y=-\frac{5}{3}x + 10\), \(y=-\frac{5}{3}\times5+10=-\frac{25}{3}+10=\frac{-25 + 30}{3}=\frac{5}{3}\approx1.67\).
• For \(y=-3x + 14\), \(y=-3\times5+14=-15 + 14=-1

eq2\).

Answer:

\(y =-\frac{5}{3}x + 10\)