Variation and Rates of Change A

numberandalgebra path stn adv

Variation and rates of change A (Path) | NSW curriculum Website

• MA5-RAT-P-01 identifies and solves problems involving direct and inverse variation and their graphical representations

📖 Prior Knowledge

Content	Prior knowledge	Used for
Ratios and Rates	- rates	- direct variation
Equations A	- solving multistep equations	- solving equations involving direct and inverse variation
Linear Relationships A	- graphs of straight lines	- direct variation graphs

Identify and describe problems involving direct and inverse variation.pdf

• 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 inversely proportional to $x$, $y$ varies inversely as $x$
• Identify and represent inverse variation/proportion as  $y\propto \frac{1}{x}$ ($y$ is inversely proportional to $x$) or $y=\frac{k}{x}$, where $k$ is the constant of variation

Identify and describe graphs involving direct and inverse variation.pdf

• 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 $k$ 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.pdf

• 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