To find the equation of the trend line using the two yellow points, let's proceed with the following steps:

1. Identify the Coordinates of the Yellow Points:

   • From the image, the yellow points are approximately at $(1, 5)$ and $(5, 7)$.

2. Calculate the Slope (m): The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the values from the points $(1, 5)$ and $(5, 7)$: $m = \frac{7 - 5}{5 - 1} = \frac{2}{4} = \frac{1}{2}$

3. Use the Point-Slope Form to Find the Equation: With the slope $m = \frac{1}{2}$ and using the point $(1, 5)$, the point-slope form of the line is: $y - y_1 = m(x - x_1)$ Substituting in the values: $y - 5 = \frac{1}{2}(x - 1)$

4. Simplify to Slope-Intercept Form (y = mx + b): Expanding and simplifying: $y - 5 = \frac{1}{2}x - \frac{1}{2}$ $y = \frac{1}{2}x + \frac{9}{2}$

So, the equation of the trend line in slope-intercept form is: $y = \frac{1}{2}x + \frac{9}{2}$

Would you like more details on any specific part of the solution?

Related Questions

1. How do you calculate the slope of a line between two points?
2. What is the point-slope form of a linear equation?
3. How can you convert from point-slope form to slope-intercept form?
4. What is the significance of the y-intercept in a line equation?
5. How can you determine the best trend line for a scatter plot with more data points?

Tip:

When finding the equation of a line, ensure you accurately determine the coordinates of the points used to calculate the slope to improve precision.