Question

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

Explanation:

In the context of linear equations (specifically the slope - intercept form \(y = mx + b\), where \(m\) is the slope), when the slope \(m\) is positive, as the value of \(x\) (the independent variable) increases, the value of \(y\) (the dependent variable) also increases. This results in the line on the coordinate plane rising from left to right. For example, if we have a line with the equation \(y=2x + 1\), the slope \(m = 2\) (which is positive). When \(x = 1\), \(y=3\); when \(x = 2\), \(y = 5\). As \(x\) increases from 1 to 2, \(y\) increases from 3 to 5, and the line rises.

Answer:

positive