7. Solve this equation for y: 7y=12x

Question

(1 point)
Responses

y=712x
y is equal to 7 over 12 x

y=12x−7
y is equal to 12 x minus 7

y=12x+7
y is equal to 12 x plus 7

y=127x
y is equal to 12 sevenths x
Question 2
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

Bud
Bud

Bob
Bob

Bill
Bill

None of them are correct
None of them are correct
Question 3
9. Solve 3x+2b=6c
for x.

Step 1: 3x+2b−2b=6c−2b
subtract 2b from both sides

Step 2: 3x=6c−2b
combine like terms/simplify

Step 3: 3x3=6c3−2b
divide by 3 on both sides to get x isolated

Step 4: x=2c−2b
simplify/final answer

Which statement is TRUE?

(1 point)
Responses

The process is correct.
The process is correct.

The process has an error. The correct answer is x=4bc3
The process has an error. The correct answer is x is equal to the fraction with numerator 4 b c and denominator 3

The process has an error. The correct answer is x=2c−23b
The process has an error. The correct answer is x is equal to 2 c minus 2 thirds b

The process has an error. The correct answer is x=−4b−c
The process has an error. The correct answer is x is equal to negative 4 b minus c
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Answer 1

Question 1

To solve the equation \(7y = 12x\) for \(y\):

1. Divide both sides by 7: \[ y = \frac{12x}{7} \] So the correct answer is: y is equal to \(\frac{12}{7} x\).

Question 2

To change the equation \(8x - 4y = 24\) into slope-intercept form (y = mx + b):

1. Subtract \(8x\) from both sides: \[ -4y = -8x + 24 \]
2. Divide by \(-4\): \[ y = 2x - 6 \]

Therefore, Bob's answer is correct: Bob.

Question 3

To solve the equation \(3x + 2b = 6c\) for \(x\):

1. Subtract \(2b\) from both sides: \[ 3x = 6c - 2b \]
2. Divide by \(3\): \[ x = \frac{6c - 2b}{3} \] This can be further simplified to: \[ x = 2c - \frac{2b}{3} \]

The initial steps in the process are correct, but Step 4 does not provide the correct simplified form. Therefore, the correct interpretation of the response is:

The process has an error. The correct answer is \(x = 2c - \frac{2}{3}b\).