Zero Slope

Zero slope refers to a line parallel to the x-axis of the coordinate system. The line with zero slope makes an angle of 0º or 180º with the positive direction of the x-axis. Any two points on a line with zero slope has the same value for the y coordinates. The line with zero slope cuts the y-axis at the point (0, a), and it is at a distance of 'a' units form the x-axis.

Let us learn more about the zero slope, the graph of the zero slope, how to calculate the slope, with the help of examples, FAQs.

Zero slope refers to a line which is a perfectly horizontal line and is parallel to the x-axis. A line with a zero slope has m = 0 and the angle θ = 0º or 180º with respect to the positive x-axis. The rise to run ratio of a line with a zero slope is zero. Here the rise is the change in y value, which is represented as Δy ad is equal to zero, and the run is the change in x value, which is represented as Δx. A zero slope signifies that the y coordinates of the two given points are equal to a constant value. Here we have y₁=y₂, and Δy = y₂ - y₁ = 0.

Zero Slope (m) = rise/run = Δy/Δx = 0

A zero slope signifies that one of the two variables which is represented along the y-axis is constant. Here as the x value changes, but the y value remains constant for all the points on the line with a zero slope. The rise to run ratio of a line with zero slope is also zero, since the rise, or the change in y value, ie .Δy=0. The tangent angle of the line with zero slope is always zero.

m = Tan0º = 0

The line with a zero slope is a perfectly horizontal line and it cuts the y-axis at one distinct point. If the line with zero slope is cutting the y-axis at the point (0, a), then it is at a distance of 'a' units from the x-axis. The line which is not horizontal is either having a negative slope or a positive slope.

The graph of zero slope shows that one of the values is a constant value. The two quantities are represented graphically across the x-axis and the y-axis, and this line with zero slope has the quantity represented along the y-axis which is constant. The value of the quantity represented along the x-axis changes, but the value of the other quantity represented along the y-axis is constant. This constant relation is represented by the blue line in the below graph, with a zero slope.

Graphically the line with a zero slope is a horizontal line, which is parallel to the x-axis, and it cuts the y-axis at one distinct point. Since it is a horizontal line it makes an angle of 0º with respect to the x-axis.The line having an angle more than 0º has a positive slope.

The zero slope of a line can be computed using three simple methods. The zero slope of a line can be computed either from the points on the line, from the angle made by the line with the positive x-axis, or from the derivative of the equation of the line/curve. For the two points \((x_1, y_1)\) and \((x_2, y_2)\) on the line, the slope can be calculated using the formula m = \(\dfrac{(y_2 - y_1)}{(x_2 - x_1)}\).

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 zero slope is 0º or 180º. And we compute the slope using the formula m = Tan0º = Tan180º = 0.

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.

☛Related Topics

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

What Is The Line With Zero Slope?

Zero slope refers to a line that is a horizontal line and is parallel to the x-axis. The angle made by a line with a zero slope is 0º or 180º, with the positive x-axis. A line with zero slope refers to a constant value represented along the y-axis, and which does not change across the points on the line.

What Can We Understand If A Line Is With Zero Slope?

The zero slope signifies that the line is a horizontal line and is parallel to the x-axis. Here the x coordinate values across any of the points on the line are distinct, and the y coordinate values across the points on the line are equal to a constant value.

What Is The Relationship Between A-Line With Zero Slope And The Coordinate Axis?

The line with zero slope is a horizontal line that is parallel to the x-axis, and it is perpendicular to the y-axis. The line with zero slope only cuts the y-axis at one distinct point. If the line with zero slope cuts the y-axis at the point (0, a), then it is at a distance of a units from the x-axis.

How Can We Identify A Line With Zero Slope From A Line With Positive OR Negative Slope?

The line with zero slope is a perfectly horizontal plane line, but the line with a positive slope is inclined upwards as we observe from left to right. And the line with a negative slope is also inclined and is sloping downwards from left to right.

What Is The Relationship Between The Coordinates Of The Points For A Line With Zero Slope?

For a line with a zero slope and passing through the two points \((x_1, y_1)\) and \((x_2, y_2)\), the y coordinate values are always equal, y₁ = y_2.

How To Calculate Zero Slope From The Given Points?

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.For a line with zero slope we have y₁=y₂, and hence we have m = 0.