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What is the equation of the line that passes through the points (1, 2) and (3, 6

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Question: What is the equation of the line that passes through the points (1, 2) and (3, 6)?

Options:

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

Correct Answer: y = 2x

Solution: 

Calculate the slope: m = (y2 - y1)/(x2 - x1) = (6 - 2)/(3 - 1) = 2.\\nUsing point-slope form: y - 2 = 2(x - 1) gives y = 2x.

What is the equation of the line that passes through the points (1, 2) and (3, 6

Practice Questions

Q1
What is the equation of the line that passes through the points (1, 2) and (3, 6)?
  1. y = 2x
  2. y = 3x - 1
  3. y = 4x - 2
  4. y = x + 1

Questions & Step-by-Step Solutions

What is the equation of the line that passes through the points (1, 2) and (3, 6)?
  • Step 1: Identify the two points given. The points are (1, 2) and (3, 6).
  • Step 2: Label the points. Let (x1, y1) = (1, 2) and (x2, y2) = (3, 6).
  • Step 3: Calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1).
  • Step 4: Substitute the values into the slope formula: m = (6 - 2) / (3 - 1).
  • Step 5: Simplify the calculation: m = 4 / 2 = 2.
  • Step 6: Use the point-slope form of the equation: y - y1 = m(x - x1).
  • Step 7: Substitute m, x1, and y1 into the point-slope form: y - 2 = 2(x - 1).
  • Step 8: Simplify the equation: y - 2 = 2x - 2.
  • Step 9: Add 2 to both sides to solve for y: y = 2x.
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