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Bot GPT 4-o mini You're on the right track with rewriting your equation! Let's take it step by step to help you transform the equation and find the correct form for \( y \).
Starting with your equation:
\[
-x + \frac{1}{4}y + \frac{5}{4} = 0
\]
To eliminate the fractions, the common denominator for the terms with the fractions is 4. Multiply the entire equation by 4:
\[
4(-x) + 4\left(\frac{1}{4}y\right) + 4\left(\frac{5}{4}\right) = 0
\]
This simplifies to:
\[
-4x + 1y + 5 = 0
\]
Now, we can write it in a clearer form:
\[
-y + 4x + 5 = 0
\]
To make it look like \( Ax + By + C = 0 \) and isolate \( y \), let's rearrange the equation to get \( y \) on one side. Move \( 4x \) and \( 5 \) to the right:
\[
y = 4x + 5
\]
So, we indeed have:
\[
y = 4x + 5
\]
Next, since you want \( y \) in terms of \( x \) and you mentioned \( x = 5 \), let's substitute \( x \) with \( 5 \):
\[
y = 4(5) + 5
\]
Calculating gives:
\[
y = 20 + 5 = 25
\]
It looks like there was a misunderstanding with the \( y \) value you might have provided (15 does not match 25 as per the substitution).
However, if you want your final equation in the specified format with \( Ax + By + C = 0 \) and only one sign you can rearrange it like this:
Starting from:
\[
y - 4x - 5 = 0
\]
To maintain the form you indicated would prefer to be:
\[
4x - y + 5 = 0
\]
This is still equivalent but emphasizes \( Ax + By + C = 0 \) where \( A = 4 \), \( B = -1 \), and \( C = 5 \). Let me know if you have further questions or need more explanation on any step!