Question

a ______ slope means that the line falls as x increases.

Explanation:

Step1: Recall slope properties

In the slope - intercept form of a line \(y = mx + b\), where \(m\) is the slope. If \(m>0\), the line rises as \(x\) increases (positive slope). If \(m < 0\), the line falls as \(x\) increases (negative slope). A slope of \(m = 0\) means the line is horizontal (neither rising nor falling), and an undefined slope (when the line is vertical) is not applicable here as we are talking about a line that falls as \(x\) increases.

Step2: Determine the type of slope

Since the line falls as \(x\) increases, the slope must be negative.

Answer:

negative