QQuestionMathematics
QuestionMathematics
The linear equation y=−2 is a horizontal line and has an undefined slope.
True
False
12 months agoReport content
Answer
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Step 1:I'll solve this step by step with precise mathematical reasoning:
Step 2:: Recall the definition of slope
m = \frac{\Delta y}{\Delta x}
The slope of a line represents the change in y divided by the change in x, mathematically expressed as:
Step 3:: Analyze the given equation y = - 2
This equation represents a horizontal line where: - The y-coordinate is always - 2 - The x-coordinate can be any real number - No matter what x-value changes, y remains constant at - 2
Step 4:: Calculate slope
m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{(-2) - (-2)}{1 - 0} = \frac{0}{1} = 0
If we choose any two points on this line, say (0, - 2) and (1, - 2):
Step 5:: Evaluate the statement
The slope is 0, not undefined. Therefore, the statement is FALSE.
Final Answer
The line y = - 2 has a slope of 0, not an undefined slope. Key Insight: A horizontal line always has a slope of 0, which means for any change in x, there is no change in y.
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