Question

investigating the slope of the line
use the slider to change the value of m
as the value of m changes from 1 to 3, the graph
changes from -6 to -1, the graph
gets less steep
negative, the slope of the line is
gets steeper
moves down
moves up

Explanation:

1. For when \(m\) changes from 1 to 3: A larger positive slope means the line becomes steeper, as the rate of vertical increase per horizontal unit grows.
2. For when \(m\) changes from -6 to -1: As the negative slope moves closer to 0, the line becomes less steep, since the magnitude of the slope decreases.
3. When the slope is negative, the line moves down from left to right, as a negative slope means vertical decrease with horizontal increase.

Answer:

1. As the value of \(m\) changes from 1 to 3, the graph gets steeper
2. As the value of \(m\) changes from -6 to -1, the graph gets less steep
3. When the slope of the line is negative, the graph moves down