We will now concentrate on the meaning of m and b in the linear equation y = mx + b by trying different values for m and b. To do this we might enter the following lines in the input field at the screen's bottom and press the Enter key at the end of each line.
m = 1
b = 2
y = m x + b
Now we can change m and b using
the input field or directly in the algebra window by right clicking (MacOS: Apple
+ click) one of the numbers and selecting Redefine. Try the following values for m
and b.
m = 2
m = -3
b = 0
b = -1
Also, you can change m and b very easily using
· the arrow keys (see Animation)
·
sliders: right click (MacOS: Apple +
click) on m or b and select Show / hide object (also see mode
Slider)
·
In a similar way we might investigate the equations of conic sections such as
· ellipses: x^2/a^2 + y^2/b^2 = 1
· hyperbolas: b^2 x^2 – a^2 y^2 = a^2 b^2 or
· circles: (x - m)^2 + (y - n)^2 = r^2
Related Topics