Online Mathematics Book

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: \[y = \frac{x}{2}-3\]

Answers Without Working