1. Drawing a line

Drawing a line

A line that is drawn in a coordinate system can be described with an equation. The equation of a line indicates how the [[$ x $]] and [[$ y $]] coordinates of the points that make up the line depend on one another. To draw a line, you must know at least two points on the line. Usually, three points are required to draw a line, with one of the points serving as a checkpoint.

Instructions for drawing a line

Choose three suitable values of [[$ x $]].
Calculate and table the corresponding values of [[$ y $]].
Draw a coordinate system and mark the points ([[$ x $]], [[$ y $]]) on it.
Draw the line through the points.
Write the equation next to the line.

Example 1

Draw the graph of the line [[$ y = 2x $]].

Solution: First, calculate some values of [[$ y $]] with some values of [[$ x $]]. You can choose any number as the value of [[$ x $]], but it is usually best to use small numbers. When using small numbers, it will be easier to calculate the values of [[$ y $]] and place the points in the coordinate system.

[[$ x $]]	[[$ y = 2x $]]	[[$ (x, y) $]]
[[$ 0 $]]	[[$ 2 \cdot 0 = 0 $]]	[[$ (0, 0) $]]
[[$ 1 $]]	[[$ 2 \cdot 1 = 2 $]]	[[$ (1, 2) $]]
[[$ 2 $]]	[[$ 2 \cdot 2 = 4 $]]	[[$ (2, 4) $]]

Mark the points in the coordinate system and draw a line through them. Write the equation that describes the line next to it.

Example 2

Draw the lines [[$ y=4 $]] and [[$ x=\:–3 $]] in the same coordinate system.

[[$ x $]]	[[$ y = 4 $]]	There is no [[$ x $]] in the [[$ y $]]-equation.
[[$ -1 $]]	[[$ 4 $]]	The [[$ x $]]-coordinate can be given any value, but the [[$ y $]]-coordinate is always 4.
[[$ 0 $]]	[[$ 4 $]]
[[$ 1 $]]	[[$ 4 $]]

[[$ y $]]	[[$ x = -3 $]]	There is no [[$ y $]] in the [[$ x $]]-equation.
[[$ -1 $]]	[[$ -3 $]]	The [[$ y $]]-coordinate can be given any value, but the [[$ x $]]-coordinate is always -3.
[[$ 0 $]]	[[$ -3 $]]
[[$ 1 $]]	[[$ -3 $]]

Lines parallel to the coordinate axes

The graphs of lines that have the form [[$y=$]] are parallel to the [[$x$]]-axis.
The graphs of lines that have the form [[$x=$]] are parallel to the [[$y$]]-axis.