To solve the equation [tex]\(y = mx + b\)[/tex] for [tex]\(b\)[/tex], we need to isolate [tex]\(b\)[/tex] on one side of the equation. Here are the steps to manipulate the equation:
1. Start with the original equation:
[tex]\[ y = mx + b \][/tex]
2. To isolate [tex]\(b\)[/tex], we need to move [tex]\(mx\)[/tex] to the other side of the equation. To do this, we subtract [tex]\(mx\)[/tex] from both sides:
[tex]\[ y - mx = b \][/tex]
Therefore, the equation solved for [tex]\(b\)[/tex] is:
[tex]\[ b = y - mx \][/tex]
Looking at the given options:
- [tex]\( y - m = b \)[/tex]
- [tex]\( y - mx = b \)[/tex]
- [tex]\(\frac{y}{mx} = b \)[/tex]
- [tex]\(\frac{y}{m} - x = b \)[/tex]
The correct solution is:
[tex]\[ y - mx = b \][/tex]
So the correct answer is [tex]\( y - mx = b \)[/tex].
