Let's extract the information from the graph to calculate the equation of the line. The equation of a line in slope-intercept form is:

$y = mx + b$

Where:

• $m$ is the slope
• $b$ is the y-intercept

Step 1: Identify the two points on the trend line

From the image, the two blue points appear to be:

1. $(2, 4)$
2. $(8, 9)$

Step 2: Calculate the slope ($m$)

The formula for slope is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substitute the values of the points: $m = \frac{9 - 4}{8 - 2} = \frac{5}{6}$

So, the slope $m = \frac{5}{6}$.

Step 3: Use one point to find the y-intercept ($b$)

The slope-intercept form is: $y = mx + b$ Substitute $m = \frac{5}{6}$ and use the point $(2, 4)$: $4 = \frac{5}{6}(2) + b$ Simplify: $4 = \frac{10}{6} + b$ $4 = \frac{5}{3} + b$ Subtract $\frac{5}{3}$ from both sides: $b = 4 - \frac{5}{3} = \frac{12}{3} - \frac{5}{3} = \frac{7}{3}$

Step 4: Write the equation

The equation of the line is: $y = \frac{5}{6}x + \frac{7}{3}$

Final Answer:

$\boxed{y = \frac{5}{6}x + \frac{7}{3}}$

Let me know if you need further explanation!

Related Questions:

1. How do you calculate the slope if the points are given as decimals?
2. What happens to the equation if the points are shifted horizontally or vertically?
3. Can the slope-intercept form be converted to standard form?
4. How would the trend line change if additional points were included in the scatter plot?
5. Why is it important to select points that lie exactly on the trend line?

Tip:

Always double-check the points you select on a scatter plot to ensure they lie on the line to avoid calculation errors.