Question

Which equation below describes the Line of Best Fit for this graph. Use the points (4,40) and (17,170) to help you determine this.

Answer 1

To determine the equation of the Line of Best Fit using the points (4, 40) and (17, 170), we can follow these steps:

1. **Find the slope (m)** of the line using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (4, 40) and (17, 170):
- \( (x_1, y_1) = (4, 40) \)
- \( (x_2, y_2) = (17, 170) \)

\[
m = \frac{170 - 40}{17 - 4} = \frac{130}{13} = 10
\]

2. **Use the point-slope form** of the equation of a line, which is given by:

\[
y - y_1 = m(x - x_1)
\]

Using one of the points, we can plug in \( m = 10 \) and let’s use (4, 40):

\[
y - 40 = 10(x - 4)
\]

3. **Distributing and simplifying**:

\[
y - 40 = 10x - 40
\]
\[
y = 10x
\]

The equation of the Line of Best Fit for the graph using the given points is:

\[
y = 10x
\]