Outcomes
A student:

 MA5.21WM
selects appropriate notations and conventions to communicate mathematical ideas and solutions

 MA5.23WM
constructs arguments to prove and justify results

 MA5.29NA
uses the gradientintercept form to interpret and graph linear relationships
Content
 Students:
 Interpret and graph linear relationships using the gradientintercept form of the equation of a straight line
 graph straight lines with equations in the form \(y = mx+c\) ('gradientintercept form')
 recognise equations of the form \(y = mx+c\) as representing straight lines and interpret the xcoefficient \( (m) \) as the gradient, and the constant \( (c) \) as the yintercept, of a straight line
 rearrange an equation of a straight line in the form \( ax + by + c = 0 \) ('general form') to gradientintercept form to determine the gradient and the yintercept of the line
 find the equation of a straight line in the form \(y = mx+c\), given the gradient and the yintercept of the line
 graph equations of the form \(y = mx+c\) by using the gradient and the yintercept, 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
\(y=3x,\,\,\,\, y=3x+2,\,\,\,\, y=3x2 \)
\(y=\frac{1}{2}x,\,\,\,\, y=2x,\,\,\,\, y=3x \)
\(x=2,\,\,\,\, y=2 \)
(Communicating)  explain the effect of changing the gradient or the yintercept on the graph of a straight line (Communicating, Reasoning)
 find the gradient and the yintercept 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 \( y=mx+c \)