Write equations for proportional relationships

Learning Objectives Identify proportional relationships from tables and graphs. Determine the constant of proportionality (k) from given information. Write an equation in the form $y = kx$ to represent a proportional relationship. Use proportional equations to solve real-world problems. Distinguish between proportional and non-proportional relationships. Explain the meaning of the constant of proportionality in context. Ever wonder how much you'd earn if you worked for a certain number of hours at a fixed rate? 💰 Or how many ingredients you need if you double a recipe? 🤔 These are all about proportional relationships! In this lesson, you'll learn how to identify these special relationships and, most importantly, how to write mathematical equations that describe...

TermDefinitionExample Proportional RelationshipA relationship between two quantities where their ratio is constant. When one quantity changes, the other quantity changes by the same factor.If you earn $12 per hour, the ratio of total earnings to hours worked is always 12:1. Constant of Proportionality (k)The constant ratio between two proportional quantities. It is the value of the dependent variable ($y$) when the independent variable ($x$) is 1, and is found by dividing $y$ by $x$ ($k = y/x$).In the equation $y = 12x$, the constant of proportionality is $k=12$. This means for every 1 unit of $x$, $y$ increases by 12 units. Equation of a Proportional RelationshipA mathematical statement showing that two quantities, $y$ and $x$, are related by a constant factor $k$. It is always written i...

Formula for Constant of Proportionality $k = \frac{y}{x}$ To find the constant of proportionality ($k$), divide the dependent variable ($y$) by the independent variable ($x$) for any corresponding pair of values in a proportional relationship. This ratio will always be the same. Equation of a Proportional Relationship $y = kx$ Once you find the constant of proportionality ($k$), you can write the equation that describes the relationship between $y$ and $x$. This equation allows you to find any $y$ value for a given $x$ value, or vice versa. Test for Proportionality (from a table) For every pair $(x, y)$ in a table, calculate $\frac{y}{x}$. If all ratios are equal to the same constant $k$, the relationship is proportional. This rule helps you verify if a given set of...