Certainly! Let's start with the given equation in slope-intercept form:
[tex]\[ y = -\frac{3}{7} \cdot x + 3 \][/tex]
Our goal is to convert this equation into standard form, which generally looks like [tex]\( Ax + By = C \)[/tex], where [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex] are integers and [tex]\( A \)[/tex] is a positive coefficient.
1. Move the [tex]\( x \)[/tex] term to the left side of the equation:
[tex]\[ y + \frac{3}{7}x = 3 \][/tex]
2. Eliminate the fraction by multiplying every term by 7:
[tex]\[ 7y + 3x = 21 \][/tex]
3. Rewrite the equation in the form [tex]\( Ax + By = C \)[/tex]:
[tex]\[ 3x + 7y = 21 \][/tex]
The coefficient of [tex]\( x \)[/tex] in the standard form equation [tex]\( 3x + 7y = 21 \)[/tex] is:
[tex]\[ \boxed{3} \][/tex]
