To find the value of [tex]\( b \)[/tex] in the equation of the line [tex]\( y = -3x + b \)[/tex] which passes through the point [tex]\( (2, 1) \)[/tex], follow these steps:
1. Start with the general form of the equation:
[tex]\[ y = -3x + b \][/tex]
2. Substitute the coordinates of the given point [tex]\( (2, 1) \)[/tex] into the equation. Here, [tex]\( x = 2 \)[/tex] and [tex]\( y = 1 \)[/tex]. Substitute these values in:
[tex]\[ 1 = -3(2) + b \][/tex]
3. Simplify the equation:
[tex]\[ 1 = -6 + b \][/tex]
4. Solve for [tex]\( b \)[/tex]. To isolate [tex]\( b \)[/tex] on one side of the equation, add 6 to both sides:
[tex]\[ 1 + 6 = b \][/tex]
[tex]\[ b = 7 \][/tex]
Therefore, the value of [tex]\( b \)[/tex] that completes the equation of the line is [tex]\( 7 \)[/tex]. The full equation of the line is:
[tex]\[ y = -3x + 7 \][/tex]
