Question

Which two equations are equivalent to −3y=6x+4 ?(2 points) Responses y=−2x−43 y is equal to negative 2 x minus 4 thirds −3y=2x+2 negative 3 y is equal to 2 x plus 2 6x+3y=4 6 x plus 3 y is equal to 4 −6y=12x+8 negative 6 y is equal to 12 x plus 8

Answer 1

To find equations that are equivalent to the given equation \(-3y = 6x + 4\), we can manipulate the equation through algebraic operations.

1. **Rewrite in slope-intercept form (y = mx + b):**
\(-3y = 6x + 4\)
Divide both sides by -3:
\[
y = -2x - \frac{4}{3}
\]
This matches the original equation when rearranged. So \( y = -2x - \frac{4}{3} \) is equivalent.

2. **Check for another equivalent form:**
If we multiply the entire original equation by -2:
\[
6x + 3y = 4
\]
This is another form representing the same relationship.

Now let's look through the options given:

- **Option 1:** \(y = -2x - \frac{4}{3}\) (This is equivalent.)
- **Option 2:** \(-3y = 2x + 2\) (This is not equivalent since it doesn't match.)
- **Option 3:** \(6x + 3y = 4\) (This is equivalent.)
- **Option 4:** \(-6y = 12x + 8\) (This simplifies to \(y = -2x - \frac{4}{3}\) by dividing by -6, thus it's equivalent.)

Therefore, the two equations that are equivalent to \(-3y = 6x + 4\) are:
1. \(y = -2x - \frac{4}{3}\)
2. \(6x + 3y = 4\)

In summary, the equivalent equations are:
- \(y = -2x - \frac{4}{3}\)
- \(6x + 3y = 4\)