Question

undefined slope
y-axis
x-axis

Explanation:

Step1: Recall slope formula

The slope \( m \) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Analyze the graph

The line shown is vertical? Wait, no, looking at the graph labeled "Undefined Slope", wait, actually, a vertical line has undefined slope because \( x_2 - x_1 = 0 \) (denominator zero). But in the given graph, wait, the line here—wait, no, maybe I misread. Wait, the graph has a horizontal line? Wait, no, the title is "Undefined Slope", but a horizontal line has slope 0. Wait, maybe the graph is a vertical line. Wait, the x - axis and y - axis: if the line is vertical, then all points on it have the same x - coordinate. So for any two points on a vertical line, \( x_1=x_2 \), so \( x_2 - x_1 = 0 \), making the slope \( \frac{y_2 - y_1}{0} \), which is undefined. But in the given graph, maybe it's a vertical line? Wait, the user's graph: let's re - examine. The graph has x - axis and y - axis, and the line—wait, maybe the graph is a vertical line (even though the drawing might be a bit unclear). The key is that a vertical line has undefined slope because the change in x (\( \Delta x \)) is zero, and slope is \( \frac{\Delta y}{\Delta x} \), division by zero is undefined.

Answer:

The line in the "Undefined Slope" graph is a vertical line (or has a vertical orientation in terms of slope calculation), and its slope is undefined because the formula for slope \( m=\frac{y_2 - y_1}{x_2 - x_1} \) has a denominator of zero (when the line is vertical, \( x_2 - x_1 = 0 \)).