Question

write equations of the horizontal and vertical lines that pass through $(-3,12)$. the equation for the horizontal line is \boxed{}. the equation for the vertical line is \boxed{}.

Explanation:

Step1: Recall horizontal line equation

A horizontal line has a constant \( y \)-value for all \( x \). The equation is \( y = k \), where \( k \) is the \( y \)-coordinate of any point on the line. For the point \((-3, 12)\), the \( y \)-coordinate is 12. So the horizontal line equation is \( y = 12 \).

Step2: Recall vertical line equation

A vertical line has a constant \( x \)-value for all \( y \). The equation is \( x = h \), where \( h \) is the \( x \)-coordinate of any point on the line. For the point \((-3, 12)\), the \( x \)-coordinate is -3. So the vertical line equation is \( x = -3 \).

Answer:

The equation for the horizontal line is \( y = 12 \).
The equation for the vertical line is \( x = -3 \).