To convert the given point-slope form equation \( y - 5 = 3(x - 2) \) to the slope-intercept form \( y = mx + b \), we need to follow these steps:
1. Distribute the slope \(m\) on the right side:
[tex]\[
y - 5 = 3(x - 2)
\][/tex]
Distribute the 3:
[tex]\[
y - 5 = 3x - 6
\][/tex]
2. Isolate \(y\) to get it in the form \( y = mx + b \):
Add 5 to both sides:
[tex]\[
y = 3x - 6 + 5
\][/tex]
3. Simplify the expression:
Combine the constant terms on the right side:
[tex]\[
y = 3x - 1
\][/tex]
So, the linear function in slope-intercept form is:
[tex]\[ f(x) = 3x - 1 \][/tex]
Therefore, the correct choice is:
[tex]\[ f(x) = 3x - 1 \][/tex]
