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.