8. 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: y=2x+24




(1 point)
Responses

None of them are correct
None of them are correct

Bud
Bud

Bob
Bob

Bill

Answer 1

To change the equation from standard form to slope-intercept form (y = mx + b), let's solve the equation step by step.

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

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

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

So, the correct slope-intercept form of the equation is: \[ y = 2x - 6 \]

Now let's evaluate each person's work:

• Bob: \[ -4y = -8x + 24 \quad \text{(This step is correct)} \] \[ y = 2x - 6 \quad \text{(This step is also correct)} \] Bob is correct.

• Bill: \[ -4y = 16x \quad \text{(This step is incorrect; it should be -8x instead of 16x)} \] Bill is incorrect.

• Bud: \[ -4y = -8x + 24 \quad \text{(This part is correct)} \] \[ y = 2x + 24 \quad \text{(This step is incorrect; it should be -6, not +24)} \] Bud is incorrect.

Based on this evaluation, the correct answer is Bob.