Question

what is the slope of a line that is perpendicular to the line $y = 1$?
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$-1$
$1$
$0$

Explanation:

Step1: Analyze the line \( y = 1 \)

The line \( y = 1 \) is a horizontal line. The slope of a horizontal line is \( 0 \) because for any two points on the line, the change in \( y \) (rise) is \( 0 \), and the slope formula is \( m=\frac{\Delta y}{\Delta x} \), so \( m = \frac{0}{\Delta x}=0 \) (where \( \Delta x
eq0 \)).

Step2: Determine the slope of the perpendicular line

A line perpendicular to a horizontal line is a vertical line. The slope of a vertical line is undefined because for a vertical line, the change in \( x \) (run) is \( 0 \), and using the slope formula \( m=\frac{\Delta y}{\Delta x} \), we would have division by zero (since \( \Delta x = 0 \)), which is undefined.

Answer:

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