Formulae and GraphsTwo Lines
You will need to compare numerical values in these exercises. Hence:
Choose
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The first line
Input two sliders 
with the names m and c. Enter the function y=mx+c
in the Input bar. Make sure that the Grid is shown.
The second line
Input another line through points A and B by using the 
Line
through Two Points tool.
If you have no other objects, the two lines will have the variable names a
and b. Observe the equations of the lines in the Algebra View!
Place the second line on the first line
Place the points A and B on the first line in order to make the two lines overlap.
Observe the two equations in the Algebra View; the two equations
describe the same line. What is the correspondence between the equations? Could
you rewrite the second equation to the same form as the first equation?
Rewrite the equation of the second line by making y the subject. Compare it to the equation of the first line.
Place the first line on the second line
Move the points A and B.
Adjust the sliders m and c in order to place the first
line on the second line. You may want to increase the Increment
of the slider m.
Is it always possible to place the first line onto the second line? If not, in what cases is it not possible?
The equations of the lines
Right-click on one of the lines in the Algebra View. You can choose
between different ways of displaying the equation of a line, check them out.
Observe the equation of the second line when the line is vertical/horizontal!
Don't try Parametric Form...you will not understand it...at the
moment.
