Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025
Definition
Negative slope refers to the inclination or gradient of a line on a coordinate plane that decreases from left to right. It 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, and vice versa.
The slope of a line can be expressed as a negative fraction or a negative decimal value.
Negative slope lines intersect the y-axis at a point above the origin, resulting in a positive y-intercept.
Negative slope lines form a downward-sloping line, with the y-values decreasing as the x-values increase.
The steepness of a negative slope line is inversely proportional to the absolute value of the slope; a steeper line has a larger negative slope.
Review Questions
Explain how the sign of the slope (positive or negative) affects the orientation of a line on a coordinate plane.
The sign of the slope determines the orientation of a line on a coordinate plane. A positive slope indicates an upward-sloping line, where the y-values increase as the x-values increase. In contrast, a negative slope indicates a downward-sloping line, where the y-values decrease as the x-values increase. This inverse relationship between the x and y variables is a key characteristic of a line with a negative slope.
Describe the relationship between the x and y variables for a line with a negative slope.
For a line with a negative slope, the x and y variables have an inverse relationship. As the x-value increases, the y-value decreases, and vice versa. This means that the y-variable moves in the opposite direction of the x-variable. The steepness of the negative slope line is determined by the magnitude of the slope, with a larger negative value indicating a steeper downward inclination.
How can the slope-intercept form of a linear equation be used to identify the sign and magnitude of the slope for a line with a negative slope?
The slope-intercept form of a linear equation, $y = mx + b$, can be used to identify the sign and magnitude of the slope for a line with a negative slope. The slope, represented by the variable $m$, will be a negative value, indicating an inverse relationship between the x and y variables. The magnitude of the slope, or the steepness of the line, is determined by the absolute value of $m$. A larger negative value for $m$ corresponds to a steeper downward-sloping line, while a smaller negative value indicates a less steep negative slope.
Positive slope refers to the inclination or gradient of a line on a coordinate plane that increases from left to right, indicating a direct relationship between the x and y variables.
The slope-intercept form of a linear equation is $y = mx + b$, where $m$ represents the slope of the line and $b$ represents the y-intercept.
Rise over Run: 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.