Line Equations - How to Draw a Line

(How to draw a line, given its equation)

We now learn how to draw a line, given its line equation.

By the end of this section we'll know how to show, for example, that the line with equation: $y = x-4$ is the line shown here:

We start by learning the method, which consists of finding two points through which the line passes.
We then illustrate this technique with a tutorial.
Finally we consolidate what we have learnt by working through some exercise questions, each of which has both an answer key as well as a detailed video solution.

Method

Given a line equation $$y = mx + c$$, to draw the line we need two points through which the line passes.

• Point 1: the $$y$$-intercept: this is the point at which the line cuts the $$y$$-axis, its coordinates are always: $\begin{pmatrix}0,c\end{pmatrix}$ where $$c$$ can be read directly from the equation $$y=mx+c$$.
• Point 2: the $$x$$-intercept: this is the point at which the line cuts the $$x$$-axis.
To find it we follow two steps:
• Step 1: replace $$y$$ by $$0$$ in the line equation $$y=mx+c$$, so that we have: $0 = mx+c$
• Step 2: solve $$0 = mx+c$$ for $$x$$.
The value of $$x$$ found will be the $$x$$ coordinate of the $$x$$-intercept.

Note: This method is best illustrated with an example. Watch the tutorial, below, in which we see how this method works.

Tutorial

In the following tutorial we learn how to draw a line, given its equation, by finding both its $$y$$-intercept and its $$x$$-intercept.

We learn the method by drawing the line with equation: $y = 2x - 6$

Exercise

1. Draw the line with equation: $y = 2x-8$
2. Draw the line with equation: $y = -3x+12$
3. Draw the line with equation: $y = x-5$
4. Draw the line with equation: $y = \frac{x}{2}-3$
5. Draw the line with equation: $y = -2x+6$