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Linear equations

The linear equation and straight line graphs

  • Linear functions are functions whose graphs represent straight lines.
  • Linear equations can be recognised by the slope-intercept formula:
    \[ y = mx + c\] where \(m\) is the slope (or gradient) of the line and \(c\) is the \(y\)-intercept.
  • Sometimes you will need to rearrange the equation so that it is in the slope-intercept formula. For example:
    \begin{eqnarray*}
    2y - 4x &=& 10 \\
    2y &=& 10 + 4x \\
    y &=& \frac{10+4x}{2} \\
    y &=& \frac{10}{2}+ \frac{4}{2}x \\
    y &=& 5 + 2x \\
    y &=& 2x + 5
    \end{eqnarray*}
  • You can graph linear functions by drawing up a table of values and then plotting the points.