Final answer:
The statement is true. A line with a positive slope rises as it moves to the right, indicating an increasing relationship between the two variables it represents. Conversely, a line with a negative slope falls as it moves to the right, suggesting a decreasing relationship between the variables.
Step-by-step explanation:
If the line is sloping upward from left to right, it means that the slope is positive. This is a true statement. Positive slope indicates that as the x-value increases, the y-value also increases. The graph of a line with a positive slope rises as it moves to the right. In contrast, if the line is sloping downward from left to right, the slope is negative. A negative slope implies that as the x-value increases, the y-value decreases; hence the graph of the line descends as it moves to the right.
The value of the slope can tell you much about the graph of a line. A slope of zero corresponds to a horizontal line, and that horizontal line can be at a positive or negative y-value, depending on its position in the coordinate plane. A line with an undefined slope is vertical, indicating that the x-value does not change as the y-value increases or decreases.
Graphically, as the slope of a line increases, it becomes steeper; as the slope decreases, the line grows flatter. This concept applies whether the slope is initially positive or negative. A steeper incline corresponds to a higher positive slope, while a steeper decline represents a more negative slope. Understanding the slope is critical in various fields, such as economics, where it indicates the relationship between two variables. For example, a positive slope suggests a direct relationship, whereas a negative slope indicates an inverse relationship between two variables.