Question

Which expression is equivalent to 3x - 4y = 6?

A. (y = -7)
B. (y - x = 2)
C. (y = frac{3}{4}x + 2)
D. (3x - 4y = 2)

Answer 1

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.

1. Add 4y to both sides: 3x = 4y + 6.
2. 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.