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What is the equation of the line that passes through the origin and has a slope

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Question: What is the equation of the line that passes through the origin and has a slope of -1?

Options:

  1. y = -x
  2. y = x
  3. y = -2x
  4. y = 2x

Correct Answer: y = -x

Solution: 

The equation of a line through the origin with slope m is y = mx. Thus, y = -1x or y = -x.

What is the equation of the line that passes through the origin and has a slope

Practice Questions

Q1
What is the equation of the line that passes through the origin and has a slope of -1?
  1. y = -x
  2. y = x
  3. y = -2x
  4. y = 2x

Questions & Step-by-Step Solutions

What is the equation of the line that passes through the origin and has a slope of -1?
  • Step 1: Understand that a line can be described using the equation y = mx + b, where m is the slope and b is the y-intercept.
  • Step 2: Since the line passes through the origin, the y-intercept (b) is 0. This means the equation simplifies to y = mx.
  • Step 3: The problem states that the slope (m) is -1.
  • Step 4: Substitute -1 for m in the equation: y = -1x.
  • Step 5: Simplify the equation: y = -x.
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