Question

To sketch the line of best fit, follow these steps:

Use the "Line" Button:

You need a straight line that best represents the trend of the data points. The "Line" button allows you to draw this.
The "Point" button is for marking individual points, which is unnecessary for drawing the line of best fit.
Choosing Two Points for the Equation:

Look for two points that seem to be along the general trend of the data.
Good choices appear to be:
(4, 30)
(12, 80)
These points are well-spaced and follow the overall upward trend.
Finding the Slope:
Use the slope formula:

Answer 1

To find the slope (\(m\)) of the line of best fit using the two chosen points \( (4, 30) \) and \( (12, 80) \), we apply the slope formula:

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

Where:
- \((x_1, y_1) = (4, 30)\)
- \((x_2, y_2) = (12, 80)\)

Substituting in the values:

\[
m = \frac{80 - 30}{12 - 4} = \frac{50}{8} = 6.25
\]

So, the slope \(m\) is \(6.25\).

Finding the Y-Intercept:
Next, we use one of the points and the slope to find the y-intercept (\(b\)) of the line using the equation of a line:

\[
y = mx + b
\]

Using point \( (4, 30) \) and the slope we found:

\[
30 = 6.25(4) + b
\]
\[
30 = 25 + b
\]
\[
b = 30 - 25 = 5
\]

So the y-intercept \(b\) is \(5\).

Equation of the Line of Best Fit:
Now, we can put it all together to write the equation of the line of best fit:

\[
y = 6.25x + 5
\]

Plotting the Line:
To sketch the line, you would:
1. Start at the y-intercept \((0, 5)\).
2. Use the slope \(m = 6.25\) to find another point. From the y-intercept, you can rise 6.25 units up and run 1 unit to the right, landing at \((1, 11.25)\) approximately.
3. Draw a straight line through these points extending in both directions.

This line will best represent the trend of the data points you have.