Which linear function represents the line given by the point-slope equation [tex]$y+1=-3(x-5)$[/tex]?

A. [tex]$f(x)=-3x-6$[/tex]
B. [tex]$f(x)=-3x-4$[/tex]
C. [tex]$f(x)=-3x+16$[/tex]
D. [tex]$f(x)=-3x+14$[/tex]



Answer :

To determine which linear function represents the line given by the point-slope equation \( y + 1 = -3(x - 5) \), we will follow these steps:

1. Distribute the constant on the right-hand side:

Start with the given equation:
[tex]\[ y + 1 = -3(x - 5) \][/tex]

Distribute the \(-3\) through \( (x - 5) \):
[tex]\[ y + 1 = -3x + 15 \][/tex]

2. Isolate \( y \) to convert the equation into slope-intercept form (\(y = mx + b\)):

Subtract 1 from both sides to isolate \( y \):
[tex]\[ y = -3x + 15 - 1 \][/tex]

Simplify the equation:
[tex]\[ y = -3x + 14 \][/tex]

3. Identify the linear function that matches the simplified equation \( y = -3x + 14 \):

Compare this with the given options:
- \( f(x) = -3x - 6 \)
- \( f(x) = -3x - 4 \)
- \( f(x) = -3x + 16 \)
- \( f(x) = -3x + 14 \)

The correct function that matches \( y = -3x + 14 \) is:

[tex]\[ f(x) = -3x + 14 \][/tex]

Thus, the linear function that represents the given point-slope equation is:
[tex]\[ \boxed{f(x) = -3x + 14} \][/tex]