Chapter 1.3, Problem 109E

To determine

The slope using the graphical utility and comparison between slope and rate.

Answer to Problem 109E

The rate at which the line falls or rises is determined by the magnitude of the slope

Explanation of Solution

Given information:

The slopes of the lines $y=mx$ , where $m=0.5,1,2,\text{and}\text{4}$

Formula used:

  $y=mx$

Calculation:

The graph of $y=mx$ , when m is positive is given by,

  

The line which rises most quickly is given by,

  $y=4x$

The graph of $y=mx$ , when m is positive is given by,

  

The line which falls most quickly is given by,

  $y=-4x$

The rate at which the line falls or rises is determined by the magnitude of the slope. The more isthe magnitude of the slope the higher will be the rate of fall or rise.

Conclusion:

The more isthe magnitude of the slope the higher will be the rate of fall or rise.