key term - Negative Slope

Definition

Negative slope refers to the inclination of a line on a coordinate plane that slopes downward from left to right. It indicates an inverse relationship between the independent and dependent variables, where as one increases, the other decreases.

5 Must Know Facts For Your Next Test

1. Negative slope is indicated by a negative value, typically expressed as a fraction or decimal.
2. A negative slope line on a graph will have a downward trend from left to right.
3. Negative slope represents an inverse relationship between the independent and dependent variables.
4. The magnitude of the negative slope value indicates the steepness of the line's downward incline.
5. Negative slope is an important characteristic of linear functions that can be used to model real-world phenomena, such as the relationship between price and demand.

Review Questions

• Explain how the concept of negative slope relates to the characteristics of a linear function.
  • Negative slope is a key feature of linear functions, as it indicates an inverse relationship between the independent and dependent variables. A line with a negative slope will have a downward trend, meaning that as the independent variable increases, the dependent variable decreases at a constant rate. This inverse relationship is a defining characteristic of linear functions and allows them to be used to model a wide range of real-world phenomena where one variable changes in the opposite direction of another.
• Describe how the magnitude of a negative slope value affects the steepness of a line on a coordinate plane.
  • The magnitude of a negative slope value determines the steepness of a line with a downward trend. A larger negative slope value, such as -3, will result in a steeper downward incline compared to a line with a smaller negative slope value, such as -0.5. The more negative the slope, the more rapidly the dependent variable decreases in relation to an increase in the independent variable. This relationship between the magnitude of the negative slope and the steepness of the line is an important concept for understanding and interpreting linear functions.
• Analyze how the concept of negative slope can be used to model real-world relationships between variables.
  • Negative slope is a valuable tool for modeling inverse relationships between variables in real-world scenarios. For example, the relationship between price and demand for a product can be represented by a linear function with a negative slope, as an increase in price typically corresponds to a decrease in the quantity demanded. Similarly, the relationship between interest rates and the demand for loans can be modeled using a linear function with a negative slope, as higher interest rates discourage borrowing. By understanding the implications of negative slope, students can apply this concept to analyze and interpret a wide range of linear relationships in various contexts.

Related terms

Slope:

The measure of the steepness or incline of a line, calculated as the change in the y-coordinate divided by the change in the x-coordinate.

Linear Function:

A function that can be represented by a straight line on a coordinate plane, with a constant rate of change between the independent and dependent variables.

Inverse Relationship: A relationship between two variables where an increase in one variable corresponds to a decrease in the other variable, and vice versa.