The live figure above enables you to examine the family of functions:
This family has two parameters
and is called the linear family.
The live figure has two parameter controls at the right of the graph, one for each of the two parameters. The first one controls the value of the parameter m. Click the round blue button underneath this first control to see an animation showing what happens as the value of this parameter ranges between -5 and +5. You can stop the animation at any time by clicking the red Stop button and reset the values of the two parameters m and b to their original default values by clicking the green Reset button. You can change the value of the parameter m to any value between -5 and +5 by clicking at the appropriate place on the first vertical scale.
The second parameter control controls the value of the parameter b. Click the round blue button underneath this second control to see an animation showing what happens as the value of this parameter ranges between -10 and +10. You can stop the animation at any time by clicking the red Stop button and reset the values of the two parameters m and b to their original default values by clicking the green Reset button. You can change the value of the parameter b to any value between -10 and +10 by clicking at the appropriate place on the second vertical scale.