Question

Rewrite the following equation in standard form.

–7
8
y
=
–9
5
x
+
9
5

Answer 1

To rewrite the equation

\[
-\frac{7}{8}y = -\frac{9}{5}x + \frac{9}{5}
\]

in standard form (Ax + By = C), we can follow these steps:

1. Multiply both sides by -1 to eliminate the negative signs:

\[
\frac{7}{8}y = \frac{9}{5}x - \frac{9}{5}
\]

2. Next, we can eliminate the fractions by multiplying the entire equation by the least common multiple (LCM) of the denominators, which is 40.

Multiplying every term by 40 gives:

\[
40 \cdot \frac{7}{8}y = 40 \cdot \frac{9}{5}x - 40 \cdot \frac{9}{5}
\]

This simplifies to:

\[
35y = 72x - 72
\]

3. Rearranging this equation to standard form (Ax + By = C), we can move 72x to the left side:

\[
-72x + 35y = -72
\]

4. To express it in conventional form with a positive x coefficient, multiply by -1:

\[
72x - 35y = 72
\]

Now, the equation is in standard form:

\[
72x - 35y = 72
\]