Final answer:
None of the options given are equivalent to the linear equation 3x - 4y = 6. After solving the equation for y, none of the answer choices match the correct slope and y-intercept.
Step-by-step explanation:
The question asks which expression is equivalent to the linear equation 3x - 4y = 6. We can proceed to solve this equation for y to put it into the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
- Add 4y to both sides: 3x = 4y + 6.
- Divide both sides by 4 to solve for y: y = (3/4)x + 3/2.
Comparing the given options:
- Option A (y = -7) doesn't match our result.
- Option B (y - x = 2) isn't in the slope-intercept form.
- Option C (y = (3/4)x + 2) has the same slope as our result but a different y-intercept; it's the closest in form but still not correct.
- Option D (3x - 4y = 2) is a different equation altogether.
Therefore, none of the given options are equivalent to the equation 3x - 4y = 6.