Question

match the description with the correct response.
a vertical line

choose the correct answer below.

a. ( 2x - y = -5 )

b. ( x = -5 )

c. ( y = -5 )

d. ( x + y = 2 )

Explanation:

Step1: Recall vertical line equation

A vertical line has an undefined slope and its equation is of the form \( x = a \), where \( a \) is a constant. This is because for a vertical line, the \( x \)-coordinate is the same for all points on the line, while the \( y \)-coordinate can vary.

Step2: Analyze each option

• Option A: \( 2x - y = -5 \) can be rewritten as \( y = 2x + 5 \), which is a linear equation with a slope of 2 (a non - vertical line).
• Option B: \( x=-5 \) is in the form \( x = a \) (where \( a=-5 \)), so this represents a vertical line.
• Option C: \( y = - 5 \) is a horizontal line (since the \( y \)-coordinate is constant for all points on the line, and the slope is 0).
• Option D: \( x + y=2 \) can be rewritten as \( y=-x + 2 \), which has a slope of - 1 (a non - vertical line).

Answer:

B. \( x=-5 \)