Variations and rates

This lesson comprises four (4) master classes focusing on:

• Direct and inverse variations
• Constant rate graphs
• Rate of change

Content:

MA5-RAT-P-01

Identify and describe problems involving direct and inverse variation

• Describe typical examples of direct variation/proportion
• Apply the language of direct variation to everyday contexts: \( y \) is directly proportional to \( x \), \( y \) is proportional to \( x \), \( y \) varies directly as \( x \)
• Identify and represent direct variation/proportion as \( y \propto x \)  (\( y \) is proportional to \( x \)) or \( y=kx \) where \( k \)  is the constant of variation
• Describe typical examples of inverse (indirect) variation
• Apply the language of inverse variation to everyday contexts: \( y \) is inversely proportional to \( x \), \( y \) is proportional to the reciprocal of \( x \), \( y \) varies inversely as \( x \)
• Identify and represent inverse variation/proportion as \( y \propto \frac{1}{x} \) (\( y \) is inversely proportional to \( x \)) or \( y \propto \frac{k}{x} \) where \( k \) is the constant of variation

Identify and describe graphs involving direct and inverse variation

• Recognise and describe direct variation from graphs, noting that the graph of \( y=kx \) is a straight line passing through the origin, with its gradient being the constant of variation
• Recognise and describe inverse variation from graphs, noting that the graph of \( y=\frac{k}{x} \) is a curve

Solve problems involving direct and inverse variation and examine the relationship between graphs and equations corresponding to proportionality

• Solve problems involving direct or inverse variation using an equation
• Use linear conversion graphs to convert from one unit to another
• Graph equations representing direct variation, with or without digital tools