- MST-11-02 models and interprets linear relationships to solve problems and make predictions in practical contexts
📖 Prior Knowledge
| Content | Prerequisite relationships |
|---|---|
| Represents Numbers A | - Approximate decimals to a given number of places → Solve real-life linear relationship problems |
| Ratios and Rates | - Solve problems involving rates → Describe and represent direct variation |
| Equations | - Solve 2-step linear equations → Solve real-life linear relationship problems - Solve equations from formulas → Solve variation problems using an equation |
| Linear Relationships | - Graph a linear relationship → Solve real-life linear relationship problems - Graph a linear relationship → Interpret gradient–intercept form - Solve real-life linear relationship problems (revisited content) |
| Linear Relationships A | - Find the gradient of an interval → Recognise and graph direct variation |
| Linear Relationships B | - Interpret gradient–intercept form (revisited content) - Find a line’s equation from gradient and intercept (revisited content) - Graph a line using gradient and intercept (revisited content) - Find a line’s equation from its graph (revisited content) |
| Variation and Rates of Change A | - Describe and represent direct variation (revisited content) - Describe and represent inverse variation → Test for variation from a table of values - Describe and represent inverse variation → Solve variation problems using an equation - Test for variation from a table of values (revisited content) - Recognise and graph direct variation (revisited content) - Solve variation problems using an equation (revisited content) - Use linear conversion graphs (revisited content) |
Linear modelling
- Determine the -intercept and gradient of a straight line given in graphical form
- Determine the equation of a straight line of the form where is the gradient and is the -intercept
- Determine the -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 -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 produces a straight-line graph
- Explain that a direct variation relationship of the form is a graph that passes through the origin with gradient being the constant of variation
- Identify and represent direct variation of the form from descriptions of situations in which one quantity varies directly with another quantity
- Evaluate in the equations , 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 to solve problems in a variety of contexts