To find the equation of the trend line using the two yellow points, we need to determine the slope ($m$) and y-intercept ($b$) of the line.

Let's analyze the two yellow points visually from the image:

• The first yellow point is approximately at $(1, 2)$.
• The second yellow point is approximately at $(6, 7)$.

Step 1: Calculate the Slope (m)

The formula for the slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

Substituting in our points $(1, 2)$ and $(6, 7)$:

$m = \frac{7 - 2}{6 - 1} = \frac{5}{5} = 1$

So, the slope $m$ is 1.

Step 2: Determine the y-intercept (b)

Using the slope-intercept form $y = mx + b$, we can substitute one of the points and the slope to find $b$.

Let's use the point $(1, 2)$:

$2 = (1)(1) + b$

Solving for $b$:

$b = 2 - 1 = 1$

Step 3: Write the Equation

Now we have both the slope and y-intercept, so the equation of the trend line is:

$y = x + 1$

Let me know if you would like further details or have any questions!

Related Questions:

1. How would the equation change if the slope were negative?
2. What does the slope represent in the context of a scatter plot?
3. How do you determine if a trend line is a good fit for the data points?
4. Can we determine correlation from the trend line alone?
5. What other forms (besides slope-intercept) can represent a line?

Tip:

Always double-check point values when estimating coordinates from a graph to avoid small errors in calculations.