Which equation represents a line with a slope of zero?
[tex]y=2 x[/tex]
[tex]y=-\frac{1}{2} x+\frac{1}{2}[/tex]
[tex]y=4[/tex]
[tex]x=-5[/tex]
Answer (2)
The equation that represents a line with a slope of zero is y = 4 . This equation describes a horizontal line. Other equations listed have slopes that are either non-zero or undefined.
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A line with a slope of zero is a horizontal line.
The equation y = 2 x has a slope of 2.
The equation y = − 2 1 x + 2 1 has a slope of − 2 1 .
The equation y = 4 has a slope of 0, representing a horizontal line. Therefore, the answer is y = 4 .
Explanation
Understanding the Problem We are given four equations and need to determine which one represents a line with a slope of zero. Recall that a line with a slope of zero is a horizontal line, which has the form y = c , where c is a constant.
Analyzing Each Equation Let's examine each equation:
y = 2 x : This is in the form y = m x + b , where m = 2 and b = 0 . The slope is 2, so it's not a horizontal line.
y = − 2 1 x + 2 1 : This is in the form y = m x + b , where m = − 2 1 and b = 2 1 . The slope is − 2 1 , so it's not a horizontal line.
y = 4 : This can be written as y = 0 x + 4 . The slope is 0, so it is a horizontal line.
x = − 5 : This is a vertical line. The slope of a vertical line is undefined.
Identifying the Correct Equation The equation y = 4 represents a line with a slope of zero.
Examples
Understanding lines with zero slope is crucial in various real-world scenarios. For instance, consider the altitude of an airplane flying at a constant height; its altitude remains the same regardless of the horizontal distance covered. Similarly, in construction, a perfectly level surface, like a tabletop, represents a zero slope. Recognizing and applying the concept of zero slope helps in maintaining stability and consistency in numerous practical applications, from navigation to building.
