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=x+5
y equals x plus 5

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

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

y=1.35x+5.05
y equals 1.35 x plus 5.05
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Answer 1

To determine the equation of the line of best fit for the given data, we can use simple linear regression. However, I will guide you through the calculations based on the data provided in the table.

The points given are:
- (1, 5)
- (2, 9)
- (3, 10)
- (4, 10.5)
- (5, 11)

Using a spreadsheet calculator, you can apply the linear regression formula, which usually involves finding the slope (m) and y-intercept (b) in the equation \(y = mx + b\).

Here's how the calculations typically work out for such data:

1. Calculate the averages of x and y.
2. Use the formula for the slope \(m\):
\[
m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}
\]
3. Once you have \(m\), calculate the y-intercept \(b\) using:
\[
b = \bar{y} - m\bar{x}
\]

After performing these calculations (the details might vary depending on the spreadsheet you use), you will find:

- Slope (m) ≈ 1.35
- y-intercept (b) ≈ 5.05

Thus, the line of best fit for the data is approximately:

\[
y = 1.35x + 5.05
\]

Hence, the correct response is:

**y = 1.35x + 5.05**.