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Find the slope of the line represented by the equation 2x - 3y + 6 = 0.

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Question: Find the slope of the line represented by the equation 2x - 3y + 6 = 0.

Options:

  1. 2/3
  2. -2/3
  3. 3/2
  4. -3/2

Correct Answer: -2/3

Solution: 

Rearranging gives y = (2/3)x + 2, so slope = 2/3.

Find the slope of the line represented by the equation 2x - 3y + 6 = 0.

Practice Questions

Q1
Find the slope of the line represented by the equation 2x - 3y + 6 = 0.
  1. 2/3
  2. -2/3
  3. 3/2
  4. -3/2

Questions & Step-by-Step Solutions

Find the slope of the line represented by the equation 2x - 3y + 6 = 0.
Correct Answer: 2/3
  • Step 1: Start with the equation 2x - 3y + 6 = 0.
  • Step 2: Rearrange the equation to isolate y. First, move 2x and 6 to the other side: -3y = -2x - 6.
  • Step 3: Divide every term by -3 to solve for y: y = (2/3)x + 2.
  • Step 4: Identify the slope from the equation y = mx + b, where m is the slope. Here, m = 2/3.
  • Linear Equations – Understanding how to rearrange linear equations into slope-intercept form (y = mx + b) to identify the slope.
  • Slope Interpretation – Recognizing that the coefficient of x in the slope-intercept form represents the slope of the line.
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