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If the equation 2x + 3y = 12 is transformed into slope-intercept form, what is t

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Question: If the equation 2x + 3y = 12 is transformed into slope-intercept form, what is the slope of the line? (2023)

Options:

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

Correct Answer: -3/2

Exam Year: 2023

Solution: 

Rearranging the equation into slope-intercept form (y = mx + b) gives y = -2/3x + 4, where the slope (m) is -2/3.

If the equation 2x + 3y = 12 is transformed into slope-intercept form, what is t

Practice Questions

Q1
If the equation 2x + 3y = 12 is transformed into slope-intercept form, what is the slope of the line? (2023)
  1. 2
  2. -2
  3. 3/2
  4. -3/2

Questions & Step-by-Step Solutions

If the equation 2x + 3y = 12 is transformed into slope-intercept form, what is the slope of the line? (2023)
  • Step 1: Start with the original equation: 2x + 3y = 12.
  • Step 2: Isolate the term with y by subtracting 2x from both sides: 3y = -2x + 12.
  • Step 3: Divide every term by 3 to solve for y: y = (-2/3)x + 4.
  • Step 4: Identify the slope (m) from the slope-intercept form y = mx + b. Here, m = -2/3.
  • Slope-Intercept Form – The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
  • Rearranging Equations – Transforming an equation from standard form to slope-intercept form requires isolating y on one side of the equation.
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