To choose the linear function that represents the line given by the point-slope equation [tex]\( y - 5 = 3(x - 2) \)[/tex], we can convert this equation into the slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
Here are the steps:
1. Start with the given point-slope equation:
[tex]\[ y - 5 = 3(x - 2) \][/tex]
2. Distribute the slope value (3) on the right side of the equation:
[tex]\[ y - 5 = 3x - 6 \][/tex]
3. Isolate [tex]\( y \)[/tex] by adding 5 to both sides of the equation:
[tex]\[ y = 3x - 6 + 5 \][/tex]
4. Simplify the expression on the right side:
[tex]\[ y = 3x - 1 \][/tex]
Therefore, the linear function in slope-intercept form that matches the given point-slope equation is:
[tex]\[ f(x) = 3x - 1 \][/tex]
Among the provided options, the correct choice is:
[tex]\[ f(x) = 3x - 1 \][/tex]
