Question

what is the slope of the line x = 4?

a. undefined

b. 4

c. 1

d. 0

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line is calculated by \( m=\frac{y_2 - y_1}{x_2 - x_1} \), where \( (x_1,y_1) \) and \( (x_2,y_2) \) are two points on the line.

Step2: Analyze the line \( x = 4 \)

For the line \( x = 4 \), all points on this line have an \( x \)-coordinate of 4. Let's take two points, say \( (4,1) \) and \( (4,2) \). Then \( x_1 = 4 \), \( x_2 = 4 \), \( y_1 = 1 \), \( y_2 = 2 \).
Substituting into the slope formula: \( m=\frac{2 - 1}{4 - 4}=\frac{1}{0} \). Division by zero is undefined, so the slope of the line \( x = 4 \) is undefined.

Answer:

A. Undefined