## 2.2. Linear Equation y = m x + b

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

2. Examples

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