Final answer:
To rewrite the equation 7/8y = 4/5x - 7/2 in standard form, you first multiply both sides by 8, followed by 5, to eliminate the fractions, and then rearrange and multiply by -1 to get the final standard form of 32x - 35y = 140.
Step-by-step explanation:
To rewrite the equation 7/8y = 4/5x - 7/2 in standard form, we need to manipulate it so that it follows the format Ax + By = C, where A, B, and C are integers, and A is non-negative.
First, multiply both sides of the equation by 8 to eliminate the fraction on the left side:
8 * (7/8)y = 8 * (4/5)x - 8 * (7/2).
Now, the equation simplifies to:
7y = 32/5x - 28.
Next, multiply both sides by 5 to get rid of the fraction on the right side:
5 * 7y = 5 * (32/5)x - 5 * 28,
which leads to:
35y = 32x - 140.
Finally, we need to arrange the terms to get the x-term on the left side:
-32x + 35y = -140.
As standard form prefers A to be non-negative, we multiply the entire equation by -1 to get:
32x - 35y = 140
This is the equation written in standard form.