Question

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

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**.