Identify proportional relationships

Learning Objectives Define a proportional relationship and its key characteristics. Identify proportional relationships from tables of values by checking for a constant ratio. Identify proportional relationships from graphs by verifying linearity and passage through the origin. Identify proportional relationships from equations in the form y = kx. Calculate the constant of proportionality (k) for a given proportional relationship. Distinguish between proportional and non-proportional linear relationships. Have you ever noticed how some things grow or change together in a perfectly predictable way? 📈 Like how the cost of apples increases exactly with the number of apples you buy? In this lesson, we'll explore what makes a relationship 'proportional' and learn...

TermDefinitionExample Proportional RelationshipA relationship between two quantities where their ratio is constant. This means that as one quantity changes, the other quantity changes by a constant factor.If 1 apple costs $0.50, then 2 apples cost $1.00, and 3 apples cost $1.50. The ratio of cost to apples is always $0.50/1 apple. Constant of Proportionality (k)The constant ratio between two quantities in a proportional relationship. It represents the unit rate.In the relationship where cost = $0.50 × number of apples, the constant of proportionality (k) is $0.50 per apple. RatioA comparison of two quantities by division. It can be written as a fraction, with a colon, or with the word 'to'.The ratio of 3 boys to 2 girls can be written as 3/2, 3:2, or 3 to 2. RateA ratio that com...

Proportional Relationship Equation $$y = kx$$ A relationship is proportional if it can be written in the form $y = kx$, where $k$ is the constant of proportionality, and $x$ and $y$ are the two quantities. This equation shows that $y$ is directly proportional to $x$. Constant of Proportionality Formula $$k = \frac{y}{x}$$ To find the constant of proportionality ($k$), divide any $y$-value by its corresponding $x$-value (as long as $x \neq 0$). This ratio must be constant for all pairs of values in a proportional relationship. Graphical Representation of Proportionality A graph represents a proportional relationship if and only if it is a straight line that passes through the origin (0,0). This rule helps visually identify proportional relationships. The straight line...