You can make a linear function by dragging the two RED points almost anywhere on the screen (why almost?). The function will have the form
- linear(x) = Ux + C,
where U is a real number and the value of C is a real number.
Now try to build the same linear function by combining the appropriate amounts of linear term and constant term using the BLUE sliders.
Try to do this without displaying the functional form of the RED linear function you have made.
You can check your work by showing the expressions for the functions on the screen.
CHALLENGE - A student asks "How do you know that you can always make a linear function given two points?" What do you respond?
Can two points define any other kind of function?
Would rise/slant or run/slant be as good a measure of slope as rise/run? Why or why not?