7th Grade math test questions: solving proportional graphs

📚 Quick Study Guide

• 📈 Proportional Relationships: Two quantities are proportional if they have a constant ratio. This can be represented as $y = kx$, where $k$ is the constant of proportionality.
• 🧭 Constant of Proportionality (k): $k = \frac{y}{x}$. It's the ratio between the dependent variable ($y$) and the independent variable ($x$).
• 📊 Graphs of Proportional Relationships: These are straight lines that pass through the origin (0,0). The slope of the line represents the constant of proportionality.
• ✍️ Identifying Proportional Relationships from a Graph: Check if the line is straight and passes through the origin. If it does, the relationship is proportional.
• ➕ Using Proportional Relationships to Solve Problems: Set up a proportion (two equal ratios) and solve for the unknown quantity.

Practice Quiz

1. Which of the following equations represents a proportional relationship?
   1. $y = 2x + 3$
   2. $y = 5x$
   3. $y = x^2$
   4. $y = \frac{1}{x}$
2. A graph shows a straight line passing through the points (0,0) and (2,6). What is the constant of proportionality?
   1. 2
   2. 3
   3. 4
   4. 6
3. If $y$ is proportional to $x$, and $y = 10$ when $x = 2$, what is the value of $y$ when $x = 5$?
   1. 15
   2. 20
   3. 25
   4. 30
4. Which of the following graphs represents a proportional relationship?
   1. A curved line
   2. A straight line that does not pass through the origin
   3. A straight line that passes through the origin
   4. A dotted line
5. The cost of apples is proportional to the number of apples bought. If 3 apples cost $1.50, how much do 7 apples cost?
   1. $3.00
   2. $3.50
   3. $4.00
   4. $4.50
6. A map uses a scale where 1 inch represents 50 miles. If two cities are 3.5 inches apart on the map, what is the actual distance between them?
   1. 150 miles
   2. 175 miles
   3. 200 miles
   4. 225 miles
7. Which equation represents the graph that passes through the origin and the point (4, 8)?
   1. $y = x + 4$
   2. $y = 2x$
   3. $y = 4x$
   4. $y = \frac{1}{2}x$