Question

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

Explanation:

Step1: Expand the point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\). In the given equation \(y + 1=-3(x - 5)\), we can rewrite \(y+1\) as \(y-(-1)\). To get the slope - intercept form \(y=mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept), we expand the right - hand side:

$$
LATEXBLOCK0
$$

Step2: Solve for y

Subtract 1 from both sides of the equation:

$$
LATEXBLOCK1
$$

Since \(f(x)=y\), the linear function is \(f(x)=-3x + 14\).

Answer:

\(f(x)=-3x + 14\) (the option corresponding to \(f(x)=-3x + 14\))