Question

Use the table to answer the question.

x y
1 5
2 9
3 10
4 10.5
5 11
Use a spreadsheet calculator to determine the equation of the line of best fit for the data in this table. Round to the nearest hundredth, if needed.

(1 point)
Responses

y=5x+11
y equals 5 x plus 11

y=x+5
y equals x plus 5

y=1.35x+5.05
y equals 1.35 x plus 5.05

y=5.05x+1.35
y equals 5.05 x plus 1.35

Answer 1

To determine the equation of the line of best fit for the given data, we can perform a linear regression analysis. The data points are:

\[
\begin{align*}
(1, 5) \\
(2, 9) \\
(3, 10) \\
(4, 10.5) \\
(5, 11) \\
\end{align*}
\]

Using a spreadsheet calculator or a statistics tool, you would calculate the slope (m) and y-intercept (b) for a linear equation of the form \( y = mx + b \).

Here are the calculations:

1. **Calculate the means of x and y:**
- Mean of x = (1 + 2 + 3 + 4 + 5) / 5 = 3
- Mean of y = (5 + 9 + 10 + 10.5 + 11) / 5 = 9.1

2. **Calculate the coefficients:**
- Slope (m) is calculated as:
\[
m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}
\]
- Intercept (b) is calculated as:
\[
b = \text{mean of } y - m(\text{mean of } x)
\]

After performing these calculations, you would find that:

- \(m \approx 1.35\)
- \(b \approx 5.05\)

Thus, the equation of the line of best fit is:

\[
y \approx 1.35x + 5.05
\]

So, the correct response is:

**y = 1.35x + 5.05**