📚 Topic Summary
In Grade 7, understanding proportional relationships is crucial. A proportional relationship exists between two variables when their ratio is constant. When graphed on a coordinate plane, a proportional relationship forms a straight line that passes through the origin (0,0). The constant of proportionality, often denoted as $k$, represents the slope of this line and shows how much one variable changes for every unit change in the other. Identifying and graphing these relationships helps us predict and analyze real-world scenarios.
Graphing proportional relationships involves plotting points from a table of values and drawing a straight line through them. Remember, the line must pass through the origin for the relationship to be proportional. The equation representing the relationship is typically in the form $y = kx$, where $y$ and $x$ are the variables, and $k$ is the constant of proportionality.
🧠 Part A: Vocabulary
Match each term with its definition:
| Term |
Definition |
| 1. Constant of Proportionality |
A. A relationship where two quantities have a constant ratio. |
| 2. Proportional Relationship |
B. The point (0,0) on a coordinate plane. |
| 3. Origin |
C. A visual representation of data on a coordinate plane. |
| 4. Graph |
D. The constant ratio between two proportional quantities ($k$ in $y=kx$). |
| 5. Coordinate Plane |
E. A plane with two perpendicular lines (x-axis and y-axis) used to locate points. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph using the words provided: straight line, origin, constant, $y = kx$, proportional.
A __________ relationship, when graphed, forms a __________ that passes through the __________. The equation for this relationship is represented as __________, where $k$ is the __________ of proportionality.
🤔 Part C: Critical Thinking
Explain how you can determine if a graph represents a proportional relationship. What characteristics must the graph have?
