Equation Builder Worksheet
Equation Builder Worksheet
Writing Proportional Relationships • \(y = kx\)
Name:
Date:
Period:
Rule A relationship is proportional if the ratio of \(y\) to \(x\) is constant:
\(k = \frac{y}{x}\) (constant of proportionality) • \(y = kx\) (equation)
1
Tables to Equations
— Find the constant of proportionality \(k\), then write the equation.
Problem A: Running Distance
| Time, \(x\) (min) | Laps, \(y\) |
|---|
| 2 | 6 |
| 5 | 15 |
| 8 | 24 |
Constant of Proportionality: \(k = \frac{y}{x} =\)
Proportional Equation: \(y =\)
Problem B: Bakery Orders
| Boxes, \(b\) | Cookies, \(c\) |
|---|
| 3 | 36 |
| 7 | 84 |
| 10 | 120 |
Unit Rate: \(k =\)
Equation for \(c\) in terms of \(b\): \(c =\)
2
Scenarios to Equations
— Define variables, determine \(k\), and write the equation.
Problem C: A lawnmower uses 3 gallons of gasoline to mow 12 acres of grass. Let \(a\) = acres mowed and \(g\) = gallons used.
Gallons per acre (\(k = \frac{g}{a}\)):
Equation for \(g\):
\(g =\)
Gallons needed for 20 acres:
Problem D: An online music store charges $18 for every 4 album downloads. Let \(n\) = number of albums and \(t\) = total cost in dollars.
Cost per album (\(k = \frac{t}{n}\)):
Equation for \(t\):
\(t =\)
Total cost for 9 albums:
3
Graphs & Error Analysis
— Analyze representations and identify misconceptions.
Problem E: Water Tank Filling
0 2 4 x (min) 50 100 y (gal) (2, 50)
Point \((1, r)\) on this line: (1, )
Unit Rate \(k\):
Equation: \(y =\)
Problem F: Spot the Mistake
Leo looked at the pairs \((2, 6)\) and \((3, 7)\). He said: "The equation is \(y = x + 4\), so it is a proportional relationship."
Is Leo correct? Explain why or why not:
Self-Check: Does your equation pass through \((0, 0)\)? Is \(y = kx\) without adding or subtracting?
CCSS 7.RP.A.2c
