Negative slope refers to the direction of a line on a coordinate plane, where the line slopes downward from left to right. This indicates an inverse relationship between the x and y variables, where as one variable increases, the other decreases.
5 Must Know Facts For Your Next Test
A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward-sloping line.
The slope-intercept form of a line with a negative slope is $y = mx + b$, where $m$ is a negative number.
Negative slope can be used to model real-world situations where an increase in one variable leads to a decrease in another, such as the relationship between price and demand.
The steepness of a negative slope is determined by the absolute value of the slope, with steeper slopes having larger absolute values.
Negative slope can be used to identify inverse relationships between variables in linear functions and interpret the behavior of those relationships.
Review Questions
Explain how the sign of the slope (positive or negative) affects the direction of the line on a coordinate plane.
The sign of the slope determines the direction of the line on a coordinate plane. A positive slope indicates a line that slopes upward from left to right, while a negative slope indicates a line that slopes downward from left to right. This is because a positive slope means that as the x-value increases, the y-value also increases, creating an upward-sloping line. Conversely, a negative slope means that as the x-value increases, the y-value decreases, resulting in a downward-sloping line.
Describe how the slope-intercept form of a linear equation, $y = mx + b$, can be used to identify the slope and y-intercept of a line with a negative slope.
In the slope-intercept form of a linear equation, $y = mx + b$, the slope of the line is represented by the coefficient $m$. When $m$ is a negative number, it indicates that the line has a negative slope. The y-intercept of the line is represented by the constant term $b$, which is the point where the line crosses the y-axis. By analyzing the slope-intercept form of an equation with a negative slope, you can determine the direction and steepness of the line, as well as its y-intercept, which provides valuable information about the relationship between the variables.
Explain how negative slope can be used to model real-world situations and interpret the relationships between variables.
Negative slope can be used to model real-world situations where an increase in one variable leads to a decrease in another. For example, the relationship between price and demand for a product can be represented by a line with a negative slope, indicating that as the price increases, the demand for the product decreases. Similarly, the relationship between interest rates and the amount of money people are willing to borrow can be modeled using a line with a negative slope, where higher interest rates lead to a decrease in the amount of money borrowed. By understanding the meaning of negative slope in the context of these real-world situations, you can interpret the inverse relationship between the variables and make informed decisions or predictions based on the behavior of the system.
Positive slope refers to the direction of a line on a coordinate plane, where the line slopes upward from left to right. This indicates a direct relationship between the x and y variables, where as one variable increases, the other also increases.
The slope of a line can be calculated as the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between any two points on the line.