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
Bob changed the equation correctly.
Bob changed the equation correctly. The correct transformation from standard form to slope-intercept form for the equation 8x - 4y = 24 is y = 2x - 6.
To change the equation from standard form to slope-intercept form (y = mx + b), we need to isolate y on one side of the equation.
Let's go through each option and see which one is correct:
1. Bob:
Bob subtracts 8x from both sides: -4y = -8x + 24
Next, he divides both sides by -4: y = 2x - 6
Bob's solution is correct.
2. Bill:
Bill subtracts 8x from both sides: -4y = 16x
Then, he divides both sides by -4: y = -4x
Bill's solution is incorrect because he forgot to subtract the constant term (24) on the right side of the equation.
3. Bud:
Bud subtracts 8x from both sides: -4y = -8x + 24
Next, he divides both sides by -4: y = 2x + 24
Bud's solution is incorrect because he made an error in dividing by -4. The correct division should yield y = 2x - 6, as Bob correctly solved it.
Therefore, the correct answer is option 1: Bob.