It seems like you're looking for practice related to graphs of proportional relationships, which is a common topic in mathematics, particularly in middle school math curricula. While I can't provide actual lesson content or practice problems from a specific curriculum (like "unit 4 lesson 7"), I can certainly help explain the concept of proportional relationships and provide some practice problems that you can use.
Proportional Relationships
A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other quantity is constant. This can often be represented in the form of a straight line passing through the origin (0,0) when graphed on a coordinate plane.
In a proportional relationship, if you have two variables \( y \) and \( x \), the relationship can be expressed as: \[ y = kx \] where \( k \) is the constant of proportionality.
Key Characteristics:
- The graph of a proportional relationship is a straight line that passes through the origin (0,0).
- The slope of the line represents the constant of proportionality \( k \).
- The ratio \( \frac{y}{x} \) is constant for all points on the line.
Practice Problems
Problem 1
- Graph the following proportional relationships:
- \( y = 3x \)
- \( y = 0.5x \)
- \( y = 2x \)
Problem 2
- Identify whether the following pairs of quantities represent a proportional relationship. If yes, find the constant of proportionality.
- (2, 4) and (4, 8)
- (1, 2) and (3, 5)
Problem 3
- A recipe requires 2 cups of flour for every 3 cups of sugar.
- Write the equation representing the relationship between flour (f) and sugar (s).
- If you have 6 cups of sugar, how much flour will you need? Graph the relationship.
Problem 4
- A car travels 60 miles in 1 hour. Determine the following:
- What is the constant rate of speed?
- Express this relationship as an equation.
- If the car travels for 3 hours, how far does it go?
- Graph the relationship.
Problem 5
- Consider two variables, \( x \) and \( y \), such that when \( x = 4 \), \( y = 12 \) and when \( x = 5 \), \( y = 15 \). Is this a proportional relationship? Why or why not?
Answers to Practice Problems
While I can't provide detailed solutions in this response format, you can work through the problems, and if you need assistance or explanations for specific ones, feel free to ask!
If you're learning about proportional relationships, exploring graphs, or solving equations, these exercises should help reinforce those concepts. Let me know if you need more practice or further explanation on any topic!
3 answers