Linear Relationships

algebra year11 standard

Linear relationships | NSW Curriculum Website

• MST-11-02 models and interprets linear relationships to solve problems and make predictions in practical contexts

📖 Prior Knowledge

Content	Prior knowledge	Used for
Linear Relationships B	- $y=mx+c$ - linear modelling	- repeated content
Variation and Rates of Change A	- direct variation	- repeated content

Linear modelling

• Determine the $y$-intercept and gradient of a straight line given in graphical form
• Determine the equation of a straight line of the form $y=mx+c$ where $m$ is the gradient and $c$ is the $y$-intercept
• Determine the $y$-intercept and gradient from the equation of a straight line
• Construct a straight-line graph, with and without using graphing applications
• Model linear relationships and interpret the features of those relationships in a variety of contexts, noting that the $y$-intercept is the vertical intercept and the gradient is the rate of change
• Interpolate and extrapolate from a linear model in a practical context
• Identify and describe the limitations of a linear model in a practical context
• Use a spreadsheet to model a linear relationship in a variety of contexts

Direct variation

• Recognise that a direct variation relationship of the form $y=kx$ produces a straight-line graph
• Explain that a direct variation relationship of the form $y=kx$ is a graph that passes through the origin with gradient $k$ being the constant of variation
• Identify and represent direct variation of the form $y=kx$ from descriptions of situations in which one quantity varies directly with another quantity
• Evaluate $k$ in the equations $y=kx$, given one pair of values for the variables, and use the resulting formula to find other values of the variables to solve problems in a variety of contexts
• Graph and analyse equations of the form $y=kx$ to solve problems in a variety of contexts