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If the line 3x + 4y = 12 is transformed to slope-intercept form, what is the y-i

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Question: If the line 3x + 4y = 12 is transformed to slope-intercept form, what is the y-intercept?

Options:

  1. 3
  2. 4
  3. 12
  4. 0

Correct Answer: 4

Solution: 

Rearranging gives y = -3/4x + 3. The y-intercept is 3.

If the line 3x + 4y = 12 is transformed to slope-intercept form, what is the y-i

Practice Questions

Q1
If the line 3x + 4y = 12 is transformed to slope-intercept form, what is the y-intercept?
  1. 3
  2. 4
  3. 12
  4. 0

Questions & Step-by-Step Solutions

If the line 3x + 4y = 12 is transformed to slope-intercept form, what is the y-intercept?
  • Step 1: Start with the equation of the line: 3x + 4y = 12.
  • Step 2: To isolate y, first subtract 3x from both sides: 4y = 12 - 3x.
  • Step 3: Now, divide every term by 4 to solve for y: y = (12 - 3x) / 4.
  • Step 4: Split the fraction: y = 12/4 - 3x/4.
  • Step 5: Simplify the fractions: y = 3 - (3/4)x.
  • Step 6: Rewrite it in slope-intercept form: y = -3/4x + 3.
  • Step 7: Identify the y-intercept from the equation: The y-intercept is 3.
  • Slope-Intercept Form – Understanding how to convert a linear equation into the form y = mx + b, where m is the slope and b is the y-intercept.
  • Y-Intercept – Identifying the value of y when x = 0 in the slope-intercept form.
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