Question

Change the equation y=
8
5
​
x+3 to standard form.

8x−5y=3

5x−8y=−24

5x+8y=3

5x+8y=−24

Answer 1

To convert the equation \( y = \frac{8}{5}x + 3 \) to standard form, we start by rewriting it:

1. Move \( \frac{8}{5}x \) to the left side:
\[
-\frac{8}{5}x + y = 3
\]

2. To eliminate the fraction, multiply the entire equation by 5:
\[
-8x + 5y = 15
\]

3. To express this in standard form \( Ax + By = C \), where \( A \) is non-negative, we can multiply the entire equation by -1:
\[
8x - 5y = -15
\]

Now, let’s compare this with the options you gave:
- \( 8x - 5y = 3 \)
- \( 5x - 8y = -24 \)
- \( 5x + 8y = 3 \)
- \( 5x + 8y = -24 \)

None of the provided options are equivalent to \( 8x - 5y = -15 \).

However, modifying \( 8x - 5y = -15 \) could reveal more options:
- If we change it to the positive side by adding 15 to both sides, it won’t match any of your options directly either.

In conclusion, none of the provided options correspond to the standard form of the original equation. The equivalent standard form of \( y = \frac{8}{5}x + 3 \) is actually \( 8x - 5y = -15 \).