Change the equation from standard form to slope-intercept form by solving for y.

Question

8x - 4y = 24
Determine who changed the equation correctly:
Bob:
Subtract 8x from both sides: -4y = -8x + 24
Divide by -4 on both sides: y = 2x - 6
Bill:
Subtract 8x from both sides: -4y = 16x
Divide by -4 on both sides: y = -4x
Bud:
Subtract 8x from both sides: -4y = -8x + 24
Divide by -4 on both sides: -4x = -8x + 24
A. Bill
B. Bud
C. Bob
D. None of them are correct

Answer 1

To change the equation \(8x - 4y = 24\) from standard form to slope-intercept form, we need to solve for \(y\).

1. Start with the original equation: \[ 8x - 4y = 24 \]

2. Subtract \(8x\) from both sides: \[ -4y = -8x + 24 \]

3. Divide every term by \(-4\): \[ y = 2x - 6 \]

Now, we can check each person's work:

• Bob:

  • Correctly subtracts \(8x\): \(-4y = -8x + 24\)
  • Correctly divides by \(-4\): \(y = 2x - 6\)

  Bob's work is correct.

• Bill:

  • Correctly subtracts \(8x\): \(-4y = -8x + 24\)
  • Incorrectly divides: He incorrectly writes \(-4y = 16x\) (should still be \(-8x + 24\)). Therefore, Bill is incorrect.

• Bud:

  • Correctly subtracts \(8x\): \(-4y = -8x + 24\)
  • Incorrectly divides: He wrongly states \(-4x = -8x + 24\) instead of dividing both sides by \(-4\). Therefore, Bud is incorrect.

The correct answer is: C. Bob