In which situation can the slope be negative?

The situation where the slope can be negative occurs when there is a decrease in one quantity as the other increases. In the context of a graph, a negative slope indicates that as the value of the independent variable (usually represented on the x-axis) increases, the value of the dependent variable (usually represented on the y-axis) decreases. This relationship can be observed in various contexts, such as when an increase in one type of resource or input leads to a reduction in another. This is a key concept in understanding how two variables interact in a linear relationship, highlighting the inverse relationship between them that a negative slope represents.

In contrast, parallel lines would have the same slope, which means they would never intersect and could not represent a negative slope scenario. Perpendicular lines would have slopes that are negative reciprocals of each other, but again, this does not directly imply that either line specifically has a negative slope; one may, while the other does not. An increase in both quantities is characterized by a positive slope, as both values move in the same direction. Thus, only the situation where one quantity decreases as the other increases results in a negative slope.