A focused Grade 7 learning session for Graphing Proportional Relationships using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving graphing proportional relationships.
Graphing Proportional Relationships is part of Grade 7 Ratios and Proportional Relationships. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of graphing proportional relationships using models, equations, and test-style reasoning.
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Graphing Proportional Relationships, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
I can solve problems involving graphing proportional relationships.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
The graph shows a proportional relationship between hours worked and dollars earned. It passes through the origin and the point \((2,30)\). What is the unit rate (dollars per hour)?
Answer D: \($15\) per hour
The unit rate is the \(y\)-value when \(x=1\). Because \((2,30)\) is on the line through the origin, \(k=30/2=15\), so earning rate is \($15\) per hour.
The graph shows a proportional relationship. What is the unit rate (the value of \(y\) at \(x=1\))?
Answer D: \(0.5\)
A proportional relationship passes through the origin. The marked point is \((2,1)\), so the unit rate \(k = 1/2 = 0.5\). The line equation is \(y = 0.5x\).
Maya runs at a constant speed. The relationship between distance (miles) and time (hours) is proportional and passes through \((3, 18)\). How far does she run per hour?
Answer D: \(6\) miles per hour
From the point \((3,18)\), the unit rate is \(18 \div 3 = 6\) miles per hour.
A car drives at a constant speed shown by this graph with unit-rate point \((1, 0.8)\). Which equation represents this relationship?
Answer D: \(y = 0.8x\)
The unit-rate point \((1, 0.8)\) shows \(k = 0.8\), so the equation is \(y = 0.8x\).
A recipe for lemonade uses a constant ratio of sugar to water. The graph shows a proportional relationship that passes through the point \((4,6)\), where \(x\) = cups of sugar and \(y\) = cups of water. How many cups of water are needed for 8 cups of sugar?
Answer D: \(12\) cups
The unit rate is \(6 \div 4 = 1.5\). So \(y = 1.5x\). At \(x = 8\), \(y = 1.5 \times 8 = 12\) cups.
Which equation represents this proportional relationship?
Answer D: \(y = 0.7x\)
The unit-rate marker at \((1, 0.7)\) shows \(k = 0.7\). So the equation is \(y = 0.7x\).
A book club orders books in bulk at a constant price per book. If 10 books cost \($120\), how much do 15 books cost?
Answer C: \($180\)
Unit rate is \($120 \div 10 = $12\) per book. For 15 books: \(15 \times $12 = $180\).
A student solves math problems at a constant rate. The graph shows the relationship between minutes studied and problems solved. How many problems are solved in 15 minutes?
Answer D: \(9\) problems
From the marked point \((5,3)\), the unit rate is \(3 \div 5 = 0.6\) problems per minute. At \(x = 15\), \(y = 15 \times 0.6 = 9\) problems.
A store sells apples at a constant unit price. A customer buys 6 apples for \($4.50\). How much does one apple cost?
Answer D: \($0.75\)
Unit price = \($4.50 \div 6 = $0.75\) per apple.
A plumber charges a constant hourly rate, shown by this graph. What is the hourly rate in dollars per hour?
Answer A: \($0.80\) per hour
The unit-rate point \((1, 0.8)\) represents the rate at 1 hour, so the hourly rate is \($0.80\) per hour. Option B (\($1.60\)) is a distractor for students who double the marked value.
A manufacturing plant produces widgets at a constant rate. In 8 hours, 240 widgets are produced. How many widgets are produced per hour?
Answer D: \(30\) widgets per hour
Unit rate = \(240 \div 8 = 30\) widgets per hour.
