To determine the equation of the trend line from the scatter plot, we can use the two blue points provided.

1. First, I need to identify the coordinates of the blue points.

2. Then, I will use the slope formula:

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

   where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two blue points.

3. After calculating the slope, I will use the slope-intercept form of the equation of a line:

   $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept.

Let me first identify the two blue points and then calculate the slope and y-intercept. matplotlib import pyplot as plt import matplotlib.image as mpimg

Load and display the image

img_path = '/mnt/data/1738203619988fefc3gma.jpg' img = mpimg.imread(img_path)

Display the image to analyze it

plt.imshow(img) plt.axis('off') # Hide axes for better visual plt.show()Based on the image, the two blue points on the scatter plot appear to be at the coordinates:

• Point 1: $(4, 2)$
• Point 2: $(7, 6)$

To find the equation of the trend line, we will calculate the slope using the formula:

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

Substituting the coordinates $(x_1, y_1) = (4, 2)$ and $(x_2, y_2) = (7, 6)$, we can now compute the slope.

Let me calculate it for you. Coordinates of the blue points x1, y1 = 4, 2 x2, y2 = 7, 6

Calculate the slope

m = (y2 - y1) / (x2 - x1) mThe slope of the trend line is approximately $m = \frac{4}{3}$.

Now, to find the y-intercept $b$, we can use the point-slope form of the equation of a line:

$y - y_1 = m(x - x_1)$

Substitute one of the points (e.g., $(4, 2)$) and the slope $m = \frac{4}{3}$ to solve for $b$.

I'll now calculate the y-intercept. Calculate the y-intercept using the point (4, 2) b = y1 - m * x1 bThe y-intercept is approximately $b = -\frac{10}{3}$.

Thus, the equation of the trend line is:

$y = \frac{4}{3}x - \frac{10}{3}$

Would you like more details or further explanation? Here are some related questions you might find helpful:

1. How can we interpret the slope in the context of this trend line?
2. How do we find the equation of a line when only given one point and the slope?
3. What is the significance of the y-intercept in this equation?
4. How can the equation be applied to predict values for other points on the line?
5. How can the equation change if a different pair of points were used?

Tip: To graph a line, you can plot the y-intercept and then use the slope to find additional points!