To find the linear function that represents the given point-slope equation [tex]\( y - 2 = 4(x - 3) \)[/tex], we need to convert it to the slope-intercept form, which is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
Let's proceed step-by-step:
1. Start with the given point-slope equation:
[tex]\[ y - 2 = 4(x - 3) \][/tex]
2. Distribute the 4 on the right side of the equation:
[tex]\[ y - 2 = 4x - 12 \][/tex]
3. Add 2 to both sides to solve for [tex]\( y \)[/tex]:
[tex]\[ y - 2 + 2 = 4x - 12 + 2 \][/tex]
[tex]\[ y = 4x - 10 \][/tex]
So, the linear function in slope-intercept form that represents the given equation is:
[tex]\[ f(x) = 4x - 10 \][/tex]
Therefore, the correct function from the given options is:
[tex]\[ f(x) = 4x - 10 \][/tex]
So, the answer is:
[tex]\[ \boxed{f(x) = 4x - 10} \][/tex]
