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What is the equation of the line passing through the points (2, 3) and (4, 7)?

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Question: What is the equation of the line passing through the points (2, 3) and (4, 7)?

Options:

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

Correct Answer: y = 2x + 1

Solution: 

Slope m = (y2 - y1) / (x2 - x1) = (7 - 3) / (4 - 2) = 2. Using point-slope form: y - 3 = 2(x - 2) => y = 2x + 1.

What is the equation of the line passing through the points (2, 3) and (4, 7)?

Practice Questions

Q1
What is the equation of the line passing through the points (2, 3) and (4, 7)?
  1. y = 2x - 1
  2. y = 2x + 1
  3. y = 2x + 3
  4. y = 2x - 3

Questions & Step-by-Step Solutions

What is the equation of the line passing through the points (2, 3) and (4, 7)?
  • Step 1: Identify the two points given. The points are (2, 3) and (4, 7).
  • Step 2: Label the points. Let (x1, y1) = (2, 3) and (x2, y2) = (4, 7).
  • Step 3: Calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1).
  • Step 4: Substitute the values into the slope formula: m = (7 - 3) / (4 - 2).
  • 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 - 3 = 2(x - 2).
  • Step 8: Distribute the slope on the right side: y - 3 = 2x - 4.
  • Step 9: Add 3 to both sides to solve for y: y = 2x - 4 + 3.
  • Step 10: Simplify the equation: y = 2x - 1.
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