When drawing a line in a coordinate system, it is not always necessary to start by creating a table of points. In fact, a line can sometimes be drawn by merely interpreting its equation. To do this, the equation of the line is solved for [[$ y $]]. Using the normal equation-solving rules, terms other than the variable [[$ y $]] are moved to the right side of the equation.

Example 1

What is the slope of the line and what is the constant term? Is the line ascending or descending?

a) [[$ y = 2x + 1 $]]​

b) [[$ y = x \: - 6 $]]​

c) [[$ y = \: -4x +3 $]]​

Answers:

a) The slope is [[$ 2 $]] and the constant term is [[$ 1 $]]. Since the slope is positive, the line is a ascending.

b) The slope is [[$ 1 $]] and the standard term is [[$ -6 $]]. Since the slope is positive, the line is a ascending.

c) The slope is [[$ -4 $]] and the standard term is [[$ 3 $]]. Since the slope is negative, the line is descending.

To draw a line in the coordinate system, you must know the coordinates of at least two points on the line. The constant term tells the [[$ y $]] coordinate of the point at which the line intercepts the [[$ y $]] axis. The second point can be determined by the line's slope. The second point is found by moving from the point of intersection of the line and the [[$ y $]] axis as determined by the slope. This is done by moving along the [[$ x $]] axis by the number of steps determined by the slope's numerator and along the [[$ y $]] axis by the number of steps determined by the slope's denominator.

NB! The equation of a line that passes through the origin does not have a constant term, which means that it is of the form [[$ y = kx $]].

Example 2

Draw the line [[$ y = \displaystyle\frac {1} {3}x +2 $]]​ in the coordinate system based on its slope and constant term.

Example 3

Draw the line [[$ y = \: –2x + 4 $]]​ in the coordinate system based on its slope and constant term.