Graph proportional relationships

Learning Objectives Identify proportional relationships from tables and equations. Plot ordered pairs representing proportional relationships on a coordinate plane. Recognize that the graph of a proportional relationship is a straight line passing through the origin. Determine the constant of proportionality from the graph of a proportional relationship. Interpret points on the graph of a proportional relationship in context. Distinguish between graphs that represent proportional relationships and those that do not. Ever notice how the cost of apples increases steadily with each apple you buy? 🍎 What would that consistent increase look like if you drew it? In this lesson, you'll learn how to visually represent proportional relationships using graphs. Understanding the...

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 consistent multiplier.If 1 apple costs $0.50, then 2 apples cost $1.00, and 3 apples cost $1.50. The ratio of cost to apples ($0.50/1, $1.00/2, $1.50/3) is always $0.50. Constant of Proportionality (k)The constant ratio between two proportional quantities, often represented as $y/x = k$. It tells you how much 'y' changes for every unit change in 'x'.In the apple example, the constant of proportionality is $0.50 per apple. So, $k = 0.50$. Coordinate PlaneA two-dimensional plane formed by the intersection of a horizontal number line (x-axis) and a vertical number line (y-axis). It&#039...

Equation of a Proportional Relationship $y = kx$ This equation shows that the 'y' value is always the constant of proportionality 'k' multiplied by the 'x' value. 'k' is the constant ratio $y/x$. Constant of Proportionality from a Graph $k = \frac{y}{x}$ To find the constant of proportionality from a graph, pick any point (x, y) on the line (other than the origin) and divide its y-coordinate by its x-coordinate. Graphical Characteristics of Proportional Relationships A graph represents a proportional relationship if it is a straight line AND passes through the origin (0,0). These two conditions are essential. If a graph is a straight line but doesn't go through (0,0), or if it goes through (0,0) but isn't a straight l...