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 parallel to the y - axis). A line perpendicular to a vertical line is a horizontal line. Horizontal lines have a slope of \( m = 0 \).

Step2: Use the point - slope form (or slope - intercept form)

The slope - intercept form of a line is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. We know that \( m = 0 \) (because the line is horizontal) and the line passes through the point \( (-6,-2) \).
Substitute \( x=-6 \), \( y = - 2 \) and \( m = 0 \) into the slope - intercept form \( y=mx + b \):
\( -2=0\times(-6)+b \)
Simplify the right - hand side: \( -2 = 0 + b \), so \( b=-2 \).

Step3: Write the equation of the line

Since \( m = 0 \) and \( b=-2 \), the slope - intercept form of the line is \( y = 0x-2=-2 \). In function notation, \( f(x)=-2 \).

Answer:

\( f(x)=-2 \)