Explanation:

Equal Slopes in Two Regression Lines:
When the slopes of two regression lines are equal, it means that the relationship between the two variables is the same in both cases. This implies that for a unit change in the independent variable, the dependent variable changes by the same amount in both cases.

Correlation Coefficient (r):
The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where 1 indicates a perfect positive relationship, -1 indicates a perfect negative relationship, and 0 indicates no relationship.

Relationship between Equal Slopes and r:
When the slopes of two regression lines are equal, the correlation coefficient (r) will also be equal. This is because the correlation coefficient is directly related to the angle between the two regression lines. If the slopes are equal, the lines will be parallel, and the angle between them will be 0 degrees.

Implications:
1. If the slopes of two regression lines are equal, it indicates a strong linear relationship between the variables.
2. The equal slopes suggest that the variables move together in a consistent manner.
3. This information can be useful in predicting one variable based on the other.
In conclusion, when the slopes of two regression lines are equal, it implies that the correlation coefficient (r) is also equal. This relationship indicates a strong linear relationship between the variables being analyzed.