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NSW Syllabuses

Mathematics K–10 - Stage 5.2 - Number and Algebra Linear Relationships ◊

Outcomes

A student:

  • MA5.2-1WM

    selects appropriate notations and conventions to communicate mathematical ideas and solutions

  • MA5.2-3WM

    constructs arguments to prove and justify results

  • MA5.2-9NA

    uses the gradient-intercept form to interpret and graph linear relationships

Content

  • Students:
  • Interpret and graph linear relationships using the gradient-intercept form of the equation of a straight line
  • graph straight lines with equations in the form \(y = mx+c\) ('gradient-intercept form')
  • recognise equations of the form \(y = mx+c\) as representing straight lines and interpret the x-coefficient \( (m) \) as the gradient, and the constant \( (c) \) as the y-intercept, of a straight line L
  • rearrange an equation of a straight line in the form \( ax + by + c = 0 \) ('general form') to gradient-intercept form to determine the gradient and the y-intercept of the line
  • find the equation of a straight line in the form \(y = mx+c\), given the gradient and the y-intercept of the line
  • graph equations of the form \(y = mx+c\) by using the gradient and the y-intercept, and with the use of digital technologies ICT
  • use graphing software to graph a variety of equations of straight lines, and describe the similarities and differences between them, eg
    \(y=-3x,\,\,\,\, y=-3x+2,\,\,\,\, y=-3x-2 \)
    \(y=\frac{1}{2}x,\,\,\,\, y=-2x,\,\,\,\, y=3x \)
    \(x=2,\,\,\,\, y=2 \)
    (Communicating) ICTCCT
  • explain the effect of changing the gradient or the y-intercept on the graph of a straight line (Communicating, Reasoning) CCT
  • find the gradient and the y-intercept of a straight line from its graph and use these to determine the equation of the line
  • match equations of straight lines to graphs of straight lines and justify choices (Communicating, Reasoning) CCT
  • Solve problems involving parallel and perpendicular lines (ACMNA238)
  • determine that straight lines are perpendicular if the product of their gradients is –1
  • graph a variety of straight lines, including perpendicular lines, using digital technologies and compare their gradients to establish the condition for lines to be perpendicular (Communicating, Reasoning) ICTCCT
  • recognise that when two straight lines are perpendicular, the gradient of one line is the negative reciprocal of the gradient of the other line (Reasoning) CCT
  • find the equation of a straight line parallel or perpendicular to another given line using \( y=mx+c \)