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Zero Slope
Zero slope refers to a line parallel to the xaxis of the coordinate system. The line with zero slope makes an angle of 0º or 180º with the positive direction of the xaxis. Any two points on a line with zero slope has the same value for the y coordinates. The line with zero slope cuts the yaxis at the point (0, a), and it is at a distance of 'a' units form the xaxis.
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.
1.  What Is A Zero Slope? 
2.  Graph Of Zero Slope 
3.  How To Calculate Zero Slope? 
4.  Examples On Zero Slope 
5.  Practice Questions 
6.  FAQs On Zero Slope 
What Is A Zero Slope?
Zero slope refers to a line which is a perfectly horizontal line and is parallel to the xaxis. A line with a zero slope has m = 0 and the angle θ = 0º or 180º with respect to the positive xaxis. 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 y_{1}=y_{2}, and Δy = y_{2}  y_{1} = 0.
Zero Slope (m) = rise/run = Δy/Δx = 0
A zero slope signifies that one of the two variables which is represented along the yaxis 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 yaxis at one distinct point. If the line with zero slope is cutting the yaxis at the point (0, a), then it is at a distance of 'a' units from the xaxis. The line which is not horizontal is either having a negative slope or a positive slope.
Graph Of Zero Slope
The graph of zero slope shows that one of the values is a constant value. The two quantities are represented graphically across the xaxis and the yaxis, and this line with zero slope has the quantity represented along the yaxis which is constant. The value of the quantity represented along the xaxis changes, but the value of the other quantity represented along the yaxis 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 xaxis, and it cuts the yaxis at one distinct point. Since it is a horizontal line it makes an angle of 0º with respect to the xaxis.The line having an angle more than 0º has a positive slope.
How To Calculate Zero 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 xaxis, 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 xaxis 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.
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Examples of Zero Slope

Example 1: Find the point on the line with zero slope, which is at a distance of 5 units from the point (2, 3).
Solution:
The given point is (2, 3). Also, it is given that the slope of this line is zero.
Hence any other point on this line would be (a, 3).
A point which is a distance of 5 units from the point (2, 3) is the point (2 + 5, 3).
Here we have the points (2 + 5, 3) = (7, 3), and (2  5, 3) = (3, 3).
Therefore the points which are at a distance of 5 units from (2, 3), and on a line with zero slope is (7, 3), and (3, 3).

Example 2: Find the distance of a line with zero slope and is passing through the point (4, 5).
Solution:
The line with zero slope is parallel to the xaxis. This line passes through the point (4, 5).
Hence this line having the point(4, 5) is at a distance of 5 units from the xaxis.
Therefore this line with zero slope and passing through (4, 5) is a distance of 5 units from the xaxis.
FAQs on Zero Slope
What Is The Line With Zero Slope?
Zero slope refers to a line that is a horizontal line and is parallel to the xaxis. The angle made by a line with a zero slope is 0º or 180º, with the positive xaxis. A line with zero slope refers to a constant value represented along the yaxis, 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 xaxis. 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 ALine With Zero Slope And The Coordinate Axis?
The line with zero slope is a horizontal line that is parallel to the xaxis, and it is perpendicular to the yaxis. The line with zero slope only cuts the yaxis at one distinct point. If the line with zero slope cuts the yaxis at the point (0, a), then it is at a distance of a units from the xaxis.
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, y_{1} = 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 y_{1}=y_{2}, and hence we have m = 0.
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