Proportional Relationships & Constant of Proportionality
Aligned to 7.RP.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
Two quantities are proportional if their ratio is always the same constant, k. Then y = kx. On a graph it's a straight line through the origin.
Worked examples
Example 1
If 4 tickets cost $52, then k = 52 ÷ 4 = 13 ($/ticket). The rule is y = 13x, so 9 tickets cost 13 × 9 = $117.
Example 2
A recipe uses 3 cups of rice for 5 people. k = 3 ÷ 5 = 0.6 cups per person, so 12 people need 0.6 × 12 = 7.2 cups.
Example 3
A table is proportional only if y ÷ x is the same every row. (2, 6), (4, 12), (5, 16) is not — the last row gives 3.2, not 3.
Practice questions
- A recipe uses 2 cups flour per 3 cookies-dozen. Find k and the equation.
- Is y = 3x + 1 proportional? Why or why not?
- If 6 m of rope weighs 9 kg, how much does 10 m weigh?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Relaciones Proporcionales y Constante de Proporcionalidad
Dos cantidades son proporcionales si su razón siempre es la misma constante, k. Entonces y = kx. En una gráfica se representa como una línea recta que pasa por el origen.
Ejemplo 1: Si 4 boletos cuestan $52, entonces k = 52 ÷ 4 = 13 ($/boleto). La regla es y = 13x, así que 9 boletos cuestan 13 × 9 = $117.
Ejemplo 2: Una receta usa 3 tazas de arroz para 5 personas. k = 3 ÷ 5 = 0.6 tazas por persona, así que 12 personas necesitan 0.6 × 12 = 7.2 tazas.
Ejemplo 3: Una tabla es proporcional solo si y ÷ x es igual en cada fila. (2, 6), (4, 12), (5, 16) no lo es — la última fila da 3.2, no 3.
More Ratios & Proportional Relationships lessons
Teach this lesson today
An AI tutor that guides with questions instead of just giving answers — all K–12 core subjects, every child in the family.
Start free — no card required