🔑 Key Concepts
- A proportional relationship has a graph that is a straight line through the origin.
- The origin is the point \( (0,0) \).
- If a line is straight but does not pass through the origin, it is not proportional.
- If the points do not form a straight line, the relationship is not proportional.
- You can also test proportionality by checking whether \( \frac{y}{x} \) stays the same for each point.
✏️ Worked Examples
🧠 Math Vocabulary
- Proportional relationship: a relationship where two quantities have the same constant ratio.
- Origin: the point \( (0,0) \) on a coordinate plane.
- Constant of proportionality: the constant value of \( \frac{y}{x} \) in a proportional relationship.
- Straight line: a line with a constant rate of change.
- \( \frac{y}{x} \): a way to test whether the ratio between \( y \) and \( x \) stays constant.
💡 Main Idea
A graph represents a proportional relationship when it is a straight line that passes through the origin. You can often identify proportionality visually, but you can also confirm it by checking that \( \frac{y}{x} \) is the same for every point.
📚 What You Should Already Know
Students should know how to read ordered pairs, identify the origin, recognize straight lines on a graph, and simplify fractions or divide to compare values of \( \frac{y}{x} \).
🚀 What Comes Next
After identifying proportional relationships from graphs, students can write proportional equations in the form \( y = kx \), find the constant of proportionality, and compare proportional relationships from tables, graphs, equations, and word problems.
🧩 Embed This Video in Your LMS
Teachers can embed this YouTube video directly into Canvas, Google Classroom, Schoology, or another learning platform. Click below to show the embed code.