Question

use the slider to change the value of m.
as the value of m changes from 1 to 3, the graph
dropdown
as the value of m changes from -6 to -1, the graph
dropdown
if the value of m is negative, the slope of the line is
dropdown
graph of y = mx with m=1, grid from -8 to 8 on x and y axes

Explanation:

Step1: Analyze \( m \) from 1 to 3

The equation is \( y = mx \), where \( m \) is the slope. When \( m \) increases from 1 to 3 (positive values), the line becomes steeper (since a larger positive slope makes the line rise more sharply). So the graph becomes steeper.

Step2: Analyze \( m \) from -6 to -1

For negative slopes, as \( m \) increases from -6 to -1 (becomes less negative), the line becomes less steep (since a slope closer to 0 is less steep). So the graph becomes less steep.

Step3: Negative \( m \) and slope

By definition, if \( m \) is negative, the slope of the line \( y = mx \) is negative (indicating the line falls from left to right).

Answer:

1. becomes steeper
2. becomes less steep
3. negative