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
• 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
• 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)
• explain the effect of changing the gradient or the y-intercept on the graph of a straight line (Communicating, Reasoning)
• 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)
• 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)
• 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)
• find the equation of a straight line parallel or perpendicular to another given line using $$y=mx+c$$