Question

question 8 (1 point)
(02.04 lc)
what is the equation of a line that contains the points (5, 0) and (5, -2)?
a x = 5
b x = 0
c y = 0
d y = 5

Explanation:

Step1: Recall line - equation form

The general form of a line is $y - y_1=m(x - x_1)$ where $m=\frac{y_2 - y_1}{x_2 - x_1}$. Given points $(x_1,y_1)=(5,0)$ and $(x_2,y_2)=(5, - 2)$.

Step2: Calculate the slope

$m=\frac{-2 - 0}{5 - 5}=\frac{-2}{0}$, which is undefined. A line with an undefined slope is a vertical line.

Step3: Determine the line equation

For a vertical line passing through a point $(x_0,y_0)$, the equation is $x=x_0$. Since the line passes through points where $x = 5$, the equation of the line is $x = 5$.

Answer:

A. $x = 5$