Question

write the slope-intercept equation of the function f whose graph satisfies the given conditions. the graph of f passes through (-6, -2) and is perpendicular to the line whose equation is x = -12. the equation of the perpendicular line is f(x) = \boxed{}. (simplify your answer.)

Explanation:

Step1: Analyze the given line

The line \( x = -12 \) is a vertical line (since it has an undefined slope and is of the form \( x = \text{constant} \)). A line perpendicular to a vertical line is a horizontal line. Horizontal lines have a slope of \( 0 \).

Step2: Determine the equation of the horizontal line

A horizontal line passing through the point \( (-6, -2) \) has the equation \( y = -2 \) (because for a horizontal line, the \( y \)-coordinate is constant for all \( x \)-values). In function notation, this is \( f(x) = -2 \).

Answer:

\( f(x) = -2 \)