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The equation of the pair of lines through the origin with slopes m1 and m2 is:

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Question: The equation of the pair of lines through the origin with slopes m1 and m2 is:

Options:

  1. y = m1x + m2x
  2. y = (m1 + m2)x
  3. y = m1x - m2x
  4. y = m1x * m2x

Correct Answer: y = (m1 + m2)x

Solution: 

The equation of the lines can be expressed as y = (m1 + m2)x, representing the sum of the slopes.

The equation of the pair of lines through the origin with slopes m1 and m2 is:

Practice Questions

Q1
The equation of the pair of lines through the origin with slopes m1 and m2 is:
  1. y = m1x + m2x
  2. y = (m1 + m2)x
  3. y = m1x - m2x
  4. y = m1x * m2x

Questions & Step-by-Step Solutions

The equation of the pair of lines through the origin with slopes m1 and m2 is:
  • Step 1: Understand that a line through the origin has the form y = mx, where m is the slope.
  • Step 2: Recognize that if there are two lines with slopes m1 and m2, their equations are y = m1*x and y = m2*x.
  • Step 3: To express both lines together, you can combine their slopes in a single equation.
  • Step 4: The combined equation can be written as y = (m1 + m2)x, which shows the sum of the slopes.
  • Equation of Lines – Understanding how to derive the equation of lines given their slopes and the point of intersection.
  • Slope Interpretation – Interpreting the meaning of slopes in the context of lines through the origin.
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