# Lines and Axes ## Lines

You can enter a line as a linear equation in x and y or in parametric form into the Input Bar. In both cases previously defined variables (e.g. numbers, points, vectors) can be used within the equation.

Note: You can enter a line’s name at the beginning of the input followed by a colon.
Example: 2D
• Type in `g: 3x + 4y = 2` to enter line g as a linear equation.
• You can enter a line in parametric form thus: `g: X = (-5, 5) + t (4, -3)`
• Define the parameters m = 2 and b = -1. Then, you can enter the equation `h: y = m*x + b` to get a line h in y-intercept-form.

Example: 3D
• You can enter a line in parametric form thus:
• `g: X = (1, 6, 3) + λ (7, -4, 4)` ; or via
• `g: Line[(1, 6, 3), Vector[(7, -4, 4)]]`
• You can enter a line as an intersection of 2 planes, by one of the following 3 equivalent input :
• `IntersectPath[4x+7y=46,y+z=9]`
• `(4x + 7y = 46, y + z = 9)`
• `7y = 46 - 4x = 7(9 - z)`

## Axes

The two coordinate axes are available in commands using the names xAxis and yAxis.

Example: The command `PerpendicularLine[A, xAxis]` constructs the perpendicular line to the x-axis through a given point A.

## Get parameters of a line

From the line `a: 2.2 x + 3.3 y = 4.4` you'll get with

• `x(a)` the value 2.2
• `y(a)` the value 3.3
• `z(a)` the value -4.4 (because GeoGebra save the line equation as `2.2 x + 3.3 y - 4.4 = 0`.