Negative Slope

A negative slope refers to a line that is trending downwards as it moves from left to right. The rise to run ratio of a line with a negative slope is negative. It can be calculated using the formula m = (y₂ - y₁)/(x₂ - x₁) = Tan θ = f'(x) = dy/dx. The negative slope signifies that, if one quantity is decreasing another quantity is increasing.

Further, the line with a negative slope makes an obtuse angle with the positive x-axis. Let us learn more about the negative slope, its graph, calculation of negative slope, with the help of examples, and FAQs.

A negative slope signifies that the coordinates of the two given points are negatively related. A line with a negative slope has m < 0 and the angle θ made by this line with the positive x-axis is an obtuse angle θ, such that 90º < θ < 180º. The rise to run ratio of a line with a negative slope is negative. Here the rise is the change in y value, which is represented as Δy, and the run is the change in x value, which is represented as Δx.

Negative Slope = -rise/run = -Δy/Δx

A negative slope signifies that the two variables are inversely related. Here, as the x value increases the y value decreases. Alternatively, we can also observe that as the x value decreases the y value increases. Angle made by a line with a negative slope in the anti-clockwise direction with respect to the positive x-axis or a line parallel to the x-axis is an obtuse angle. This obtuse angle is greater than a right angle(90º+θ), and the slope of the line is a negative slope.

m = Tan(90º+θ) = -Tanθ

The line with a negative slope is trending downwards from left to right. This can be observed in the negative slope graph.

The concept of the negative slope gives an inverse relationship between two quantities. The two quantities are represented graphically across the x-axis and the y-axis, and the line is plotted to represent the relationship between these two variables. As the value of the quantity represented along with the x-axis increases, the value of the other quantity represented along with the y-axis decreases. The inverse relationship of the increase of the x value, and the decrease of the y value is represented by the negative slope of the line.

A negative slope graph is a line with a negative slope, which falls as it moves from left to right. The line with a negative slope makes an obtuse angle with the positive x-axis, in the anti-clockwise direction.

The negative slope of a line can be computed using two methods. The negative slope of a line can be computed either from the points on the line or the angle made by the line with the positive x-axis. For the two points (x₁, y₁) and (x₂, y₂) on the line, the slope can be calculated using the formula m = (y₂ - y₁)/(x₂ - x₁).

Also if θ is the angle made by the line with a positive x-axis in the anticlockwise direction, the slope of the line can be computed with the tangent of this angle θ. The angle made by a line with a negative slope is always an obtuse angle and can be taken as θ=90º + α. And we compute the slope using the formula m = Tan(90º + α) = -Tanα

For a given equation of a curve f(x), the slope of the curve is the slope of the tangent at the point on the curve and is calculated by taking the differentiation of the function. m = f'(x) = dy/dx.

Let us check a few negative slope examples.

• The price of a commodity and the quantity demanded to have a negative relationship. As the price increases, the quantity purchased is decreasing and such a line has a negative slope graph.
• The age of a person and the average distance walked by the person per day if represented along the x-axis and y-axis, has a sloping line from left to right.
• The car moving down a sloping road if observed, the sloping road represents a line with a negative slope.
• The children sliding down an inclined plane has a sloping inclined plane which is having a negative slope.

☛ Related Topics:

• Equation of Line
• Differentiation
• X and Y Coordinates
• Cartesian Plane

How Do You Compute The Negative Slope Of A Line?

Negative slope refers to the slope of a line that is sloping downwards as we are moving from left to right. The angle made by a line with a negative slope is an obtuse angle with respect to the positive x-axis. A negative slope gives an inverse relationship between two variables. As the value of the x variable increase, the value of the y variable decreases.

How To Compare Coordinates Of Two Points On A Line With Negative Slope?

For a line with a negative slope and passing through the two points \((x_1, y_1)\) and \((x_2, y_2)\), if the set of ordinates increases, the set of abscissa decrease. Here we can observe that as x₂ > x₁, we have y₂< y₁.

How To Find Negative Slope Of A Line?

The negative slope of a line can be obtained from the inclination of the line. If the inclined angle of the line with the positive x-axis, in the anti-clockwise direction, is more than 90°, then the slope of the line is negative. Also, we have m = Tan(90º + α) = -Tanα. 

How To Plot Negative Slope Graph?

The negative slope is graphed with reference to the coordinate axis, and the negative slope is computed with with respect to the positive x-axis. The negative slope graph is a line with a negative slope, and is sloping downwards as we observe.from left to right.

How To Find The Negative Slope Of A Line From The Two Given Point?

The slope of a line connecting two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula m = \(\dfrac{(y_2 - y_1)}{(x_2 - x_1)}\). The slope is the ratio of the difference between the y coordinate values, and the difference between the x coordinate values.

What Can We Derive From A Negative Slope?

The negative slope signifies that the line is sloping downwards from left to right. Here the relationship between the two variables represented in the negative slope graph along the x-axis and the y-axis is inverse. The increase in one variable results in a decrease in the other variable. Similarly, we can have lines with a zero slope, or a positive slope.

What Is The Differentiate Between Negative Slope And Positive Slope?

The negative slope and the positive slope are based on the sign of the slope value. The line with a negative slope makes an obtuse angle with respect to the positive x-axis, and a line with positive slope makes an acute angle.. The line with a negative slope is sloping downwards as it moves from left to right and the line with a positive slope is inclined as we are moving from left to right.

Give A Few Negative Slope Examples.

The few negative slope examples include the playing slie of the children in the park, the sloping road, or the graph of price and quantity.  All of these graphs has a line sloping from the left to right and hence it has a negative slope.