To find the equation solved for [tex]\( b \)[/tex] from the slope-intercept form [tex]\( y = mx + b \)[/tex], follow these steps:
1. Identify the given equation:
The given equation is:
[tex]\[
y = mx + b
\][/tex]
where [tex]\( y \)[/tex] is the dependent variable, [tex]\( m \)[/tex] is the slope of the line, [tex]\( x \)[/tex] is the independent variable, and [tex]\( b \)[/tex] is the y-intercept.
2. Rearrange the equation to isolate [tex]\( b \)[/tex]:
To isolate [tex]\( b \)[/tex], we need to perform algebraic manipulations.
3. Subtract [tex]\( mx \)[/tex] from both sides of the equation:
This step is crucial to move [tex]\( mx \)[/tex] to the other side of the equation. By doing this, we get:
[tex]\[
y - mx = b
\][/tex]
4. Conclude the result:
The equation solved for [tex]\( b \)[/tex] is:
[tex]\[
y - mx = b
\][/tex]
Therefore, the correctly solved equation for [tex]\( b \)[/tex] is:
[tex]\( y - mx = b \)[/tex]
This matches the second option provided in the question:
[tex]\[
y - mx = b
\][/tex]
