Question

graph the line that passes through the points $(-4,4)$ and $(-4,3)$ and determine the equation of the line. answer attempt 1 out of 2 equation:

Explanation:

Step1: Calculate the slope

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Given the points \((x_1,y_1)=(-4,4)\) and \((x_2,y_2)=(-4,3)\), then \(m=\frac{3 - 4}{-4-(-4)}=\frac{-1}{0}\). Since the denominator is \(0\), the slope is undefined.

Step2: Determine the equation of the line

A line with an undefined slope is a vertical line. For a vertical line passing through the point \((x_0,y_0)\), the equation is \(x=x_0\). Here \(x_0=-4\), so the equation of the line is \(x = - 4\).

Answer:

\(x = - 4\)