Question
Write y + 2 = 1/3x in standard form.
_ + _ = _
_ + _ = _
Answers
GPT-4o mini
To convert the equation \( y + 2 = \frac{1}{3}x \) into standard form, we want to rewrite it in the form \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers, and \( A \) is non-negative.
1. First, isolate \( y \) by subtracting 2 from both sides:
\[
y = \frac{1}{3}x - 2
\]
2. Next, eliminate the fraction by multiplying the entire equation by 3:
\[
3y = x - 6
\]
3. Rearranging this equation gives us:
\[
-x + 3y = -6
\]
4. Finally, we can multiply through by -1 to make the coefficient of \( x \) positive:
\[
x - 3y = 6
\]
Thus, in standard form, the equation is:
\[
1x - 3y = 6
\]
So, filling in your blanks:
\( 1 + (-3) = 6 \).
1. First, isolate \( y \) by subtracting 2 from both sides:
\[
y = \frac{1}{3}x - 2
\]
2. Next, eliminate the fraction by multiplying the entire equation by 3:
\[
3y = x - 6
\]
3. Rearranging this equation gives us:
\[
-x + 3y = -6
\]
4. Finally, we can multiply through by -1 to make the coefficient of \( x \) positive:
\[
x - 3y = 6
\]
Thus, in standard form, the equation is:
\[
1x - 3y = 6
\]
So, filling in your blanks:
\( 1 + (-3) = 6 \).