Proportion Power Worksheet
Grade 7 Math Ratios & Proportional Relationships
Proportion Power Worksheet
Determining the constant of proportionality \(k\) and writing equations in the form \(y = kx\).
Name:
Date:
Period:
Score:
The Golden Rule of Proportional Equations
Core Formula
1. The Equation Form
\(y = kx\)
\(x\) is input, \(y\) is output, and \(k\) is the constant multiplier.
2. Constant of Proportionality
\(k = \frac{y}{x}\)
Always divide the dependent value (\(y\)) by the independent value (\(x\)).
3. The 3-Step Method
- Pick any pair \((x, y)\).
- Calculate \(k = \frac{y}{x}\).
- Write \(y = (\text{value of } k)x\).
A
From Tables to Equations
Verify the constant \(k\), then write the relationship's equation.
1. Running Distance Find \(k\) & Equation
Maya runs at a steady pace. The table shows time in minutes (\(x\)) and miles completed (\(y\)).
| Time, \(x\) (min) | Distance, \(y\) (mi) |
|---|
| 10 | 1.2 |
| 20 | 2.4 |
| 30 | 3.6 |
| 40 | 4.8 |
Show work for \(k = \frac{y}{x}\):
Constant (\(k\)):
\(k = \)
Equation:
2. Bakery Cupcakes Find \(k\) & Equation
Sweet Treats Bakery sells boxes of cupcakes. Let \(c\) = cupcakes and \(d\) = total cost ($).
| Cupcakes (\(c\)) | Cost in $ (\(d\)) |
|---|
| 4 | $14.00 |
| 6 | $21.00 |
| 10 | $35.00 |
| 12 | $42.00 |
Show work for unit rate (\(\frac{d}{c}\)):
Cost Per Cupcake:
\(k = \)
Equation (\(c\) & \(d\)):
B
From Graphs to Equations
Locate a coordinate point \((x,y)\), determine \(k\), and write the equation.
Time \(t\) (s) Gal \(g\) 0 1 2 3 4 0 3 6 9 12 (1, 3) Graph 1: Water Tank Fill
3. Water Pump Rate
The graph shows water pumped over time.
Identify point \((1, k)\):
\((\) , \()\)
Calculate \(k = \frac{\text{gallons}}{\text{second}}\):
\(k = \)
Equation relating \(g\) and \(t\):
Hours \(h\) Earned \(E\) ($) 0 2 4 6 8 0 30 60 90 120 (4, 60) Graph 2: Babysitting Wages
4. Hourly Wages
The graph shows total earnings for babysitting.
Pick any point \((h, E)\):
\((\) , \()\)
Hourly rate \(k = \frac{E}{h}\):
\(k = \)
Equation relating \(E\) and \(h\):
Proportion Power • Page 1 of 2 Remember: A proportional relationship always passes through the origin \((0,0)\)
PAGE 2 Proportion Power: Real-World Applications & Analysis
Student Name:
C
Real-World Word Scenarios
Define variables, calculate the unit rate \(k\), and write the equation.
5. Electric Vehicle Charging
An electric charging station adds 75 miles of driving range for every 3 hours connected. Let \(r\) be miles of range gained and \(t\) be charging time in hours.
Rate Problem
Unit Rate \(k = \frac{\text{miles}}{\text{hour}}\):
\(k = \)
Proportional Equation:
Apply: Range in 5.5 hours?
\(r = \)
6. Farmstand Fresh Strawberries
A local berry farm charges $18.00 for a 4-pound flat of fresh strawberries. Let \(C\) represent total cost in dollars and \(p\) represent weight in pounds.
Cost per Pound
Price Per Pound (\(k = \frac{C}{p}\)):
\(k = \)
Proportional Equation:
Apply: Cost for 7 pounds?
\(C = \)
7. Recipe Flour Ratio
A sourdough recipe calls for 5 cups of flour to make 2 loaves of artisan bread. Let \(f\) be cups of flour and \(L\) be number of loaves.
Recipe Ratio
Cups Per Loaf (\(k = \frac{f}{L}\)):
\(k = \)
Proportional Equation:
Apply: Flour for 6 loaves?
\(f = \)
D
Spot the Error • Mathematical Reasoning
The Scenario: Dante was given this problem: "A printing press produces 180 posters in 4 minutes. Let \(p\) be posters and \(m\) be minutes."
Dante's Work: "I divided \(4 \div 180 = \frac{1}{45}\), so my equation is \(p = \frac{1}{45}m\)."
1. What mistake did Dante make? Explain his error:
2. Calculate correct \(k\) and write the correct equation:
Correct \(k = \)
Correct Equation:
E
Reverse Challenge • From Equation to Values
Given the proportional equation \(y = 2.4x\), fill in the missing table values and answer the conceptual question:
| \(x\) (Input) | 1 | 3 | 5 | 10 |
|---|
| \(y\) (Output) | | | | |
What does the point \((1, 2.4)\) represent?
Proportion Power • Page 2 of 2 Equation mastery: \(y = kx\) where \(k = \frac{y}{x}\)
