Let’s analyze the graphs and calculate the equations of the trend lines shown in the two scatter plots.

Graph 5

The line is linear, and we can find its equation using the slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

1. Identifying points: Two points on the line are approximately $(0, 8)$ and $(40, 0)$.
2. Slope: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 8}{40 - 0} = -\frac{8}{40} = -0.2$
3. Intercept: $b = 8$ (where the line crosses the y-axis).
4. Equation: $y = -0.2x + 8$

Graph 6

Similarly, we determine the slope and intercept for this graph.

1. Identifying points: Two points on the line are approximately $(0, 80)$ and $(10, 0)$.
2. Slope: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 80}{10 - 0} = -\frac{80}{10} = -8$
3. Intercept: $b = 80$ (where the line crosses the y-axis).
4. Equation: $y = -8x + 80$

Final Equations:

1. Graph 5: $y = -0.2x + 8$
2. Graph 6: $y = -8x + 80$

Do you have any questions or want me to clarify any part?

Related Questions:

1. What are the steps to calculate the equation of a trend line if only data points are given?
2. How can you estimate the correlation between the variables in each graph?
3. What does the negative slope in each trend line indicate?
4. How would the equations change if the axes were reversed?
5. Can you explain the practical interpretation of these trend lines in real-world scenarios?

Tip:

Always start with identifying two clear points on the line to ensure accuracy when calculating the slope and intercept!