Two-Variable Equations
Aligned to A-CED.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
Many situations relate two quantities; write an equation using both variables and graph it, labeling the axes and choosing a scale that fits the data.
Worked examples
Example 1
A gym charges $20 to join plus $5 per visit. Total cost y for x visits is y = 5x + 20. The y-intercept 20 is the join fee, and the slope 5 is the cost per visit.
Example 2
A recipe needs 2 cups flour per loaf plus 1 cup for the starter: f = 2L + 1. Each variable needs its own unit.
Example 3
Two variables do not always both make sense. In y = 5x + 20, negative x means negative visits, so the model has a domain.
Practice questions
- Write an equation for a taxi that charges $3 plus $2 per mile.
- A tank holds 500 L and drains 25 L per minute. Write y in terms of x minutes.
- For y = 4x + 10, find y when x = 3.
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
Ecuaciones de Dos Variables
Muchas situaciones relacionan dos cantidades; escribe una ecuación con ambas variables y grafícala, rotulando los ejes y eligiendo una escala que se ajuste a los datos.
Ejemplo 1: Un gimnasio cobra $20 de inscripción más $5 por visita. El costo total y para x visitas es y = 5x + 20. La intersección con el eje y, 20, es la inscripción, y la pendiente 5 es el costo por visita.
Ejemplo 2: Una receta necesita 2 tazas de harina por hogaza más 1 taza para la masa madre: h = 2P + 1. Cada variable necesita su propia unidad.
Ejemplo 3: No siempre las dos variables tienen sentido. En y = 5x + 20, una x negativa son visitas negativas, así que el modelo tiene dominio.
More Algebra 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