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 equation

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

Subtract 1 from both sides of the equation \(y + 1=-3x + 15\). So \(y=-3x+15 - 1\).

Step3: Simplify the equation

Simplify \(y=-3x+15 - 1\) to get \(y=-3x + 14\). Since \(f(x)=y\), the linear function is \(f(x)=-3x + 14\).

Answer:

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