Solve problems involving proportional relationships

Learning Objectives Identify proportional relationships from tables, graphs, and equations. Determine the constant of proportionality (unit rate) in various contexts. Write equations in the form y = kx to represent proportional relationships. Solve real-world problems involving direct proportion using various strategies. Compare and contrast different proportional relationships based on their constants of proportionality. Use proportional reasoning to make predictions and solve for unknown quantities. Ever wonder how much paint you need for a wall, or how long a road trip will take? 🚗💨 Proportional relationships help us figure it out! In this lesson, you'll learn to identify, represent, and solve problems involving proportional relationships. Understanding these rela...

TermDefinitionExample Proportional RelationshipA relationship between two quantities where their ratio is constant. This means that as one quantity increases or decreases, the other quantity changes by the same factor.If 2 pencils cost $1, then 4 pencils cost $2. The ratio of cost to pencils is always $0.50/pencil, which is constant. Constant of Proportionality (Unit Rate)The constant ratio between two quantities in a proportional relationship. It represents the value of one quantity per unit of the other quantity, often denoted by 'k'.If a car travels 60 miles in 1 hour, the constant of proportionality (speed) is 60 miles/hour. So, k = 60. Direct VariationAnother name for a proportional relationship, emphasizing that one variable varies directly with another. It is represented...

Equation of a Proportional Relationship $y = kx$ This equation represents a proportional relationship where 'y' is directly proportional to 'x', and 'k' is the constant of proportionality. It shows that y is always k times x. Calculating the Constant of Proportionality $k = \frac{y}{x}$ To find the constant of proportionality 'k', divide the 'y' value by the corresponding 'x' value for any point (x, y) in the relationship (where x is not zero). Proportion Equality (Cross-Multiplication) $\frac{a}{b} = \frac{c}{d} \implies ad = bc$ When two ratios are equal (a proportion), the product of the means equals the product of the extremes. This rule is used to solve for an unknown variable in a proportion.