Question

which linear function represents the line given by the point - slope equation $y + 1=-3(x - 5)$?
$\bigcirc$ $f(x)=-3x - 6$
$\bigcirc$ $f(x)=-3x - 4$
$\bigcirc$ $f(x)=-3x + 16$
$\bigcirc$ $f(x)=-3x + 14$

Explanation:

Step1: Expand the point - slope form

We start with the point - slope equation \(y + 1=-3(x - 5)\). Using the distributive property \(a(b - c)=ab - ac\), where \(a=-3\), \(b = x\) and \(c = 5\), we get \(y+1=-3x+15\).

Step2: Solve for y (or f(x))

Subtract 1 from both sides of the equation \(y + 1=-3x+15\). So \(y=-3x + 15-1\). Simplifying the right - hand side, we have \(y=-3x+14\). Since \(y = f(x)\) for a linear function, \(f(x)=-3x + 14\).

Answer:

\(f(x)=-3x + 14\) (the fourth option: \(f(x)=-3x + 14\))