#Algebra #Year11 #Standard
>[!info]- [Linear relationships | NSW Curriculum Website](https://curriculum.nsw.edu.au/learning-areas/mathematics/mathematics-standard-11-12-2024/content/n11/fabe84d89c)
>- 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
lt;br>- 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 $y=mx+c$Â where $m$Â 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