I can write an equation from a table or a graph to model the relationship between the dependent and independent variables.Puedo escribir una ecuación a partir de una tabla o una gráfica para representar la relación entre las variables dependiente e independiente.
MissionMisión · Orbit StationEstación orbital
Mission control needs your math.El control de la misión necesita tus matemáticas.
Orbit Station runs on steady rates: kilometers per minute, liters per day, energy per hour. Turn each pattern from a table into an equation, so mission control can find any value without building a new table.
La Estación Órbita funciona con tasas constantes: kilómetros por minuto, litros por día, energía por hora. Convierte cada patrón de una tabla en una ecuación, para que el control de la misión pueda hallar cualquier valor sin armar una tabla nueva.
Word bankBanco de palabras 5 words5 palabrasequation, variable, rate, …ecuación, variable, tasa, …
- equationecuación
- A math sentence with an equals sign, like d = 9m, that shows how two quantities are related.Una oración matemática con un signo igual, como d = 9m, que muestra cómo se relacionan dos cantidades.
- variablevariable
- A letter for a quantity that can change.Una letra para una cantidad que puede cambiar.
- ratetasa
- A fixed amount for every one unit, like 9 kilometers per minute.Una cantidad fija por cada una unidad, como 9 kilómetros por minuto.
- define the variablesdefinir las variables
- Say exactly what each letter stands for, like 'Let m = minutes'.Decir exactamente qué representa cada letra, como «Sea m = minutos».
- constantconstante
- A number in an equation that never changes, like the 9 in d = 9m.Un número en una ecuación que nunca cambia, como el 9 en d = 9m.
Stage 1 of 5Etapa 1 de 5
Get ReadyPrepárate
Wake up what you know, then explore today's model.
Activa lo que sabes y luego explora el modelo de hoy.
- A ride costs $4 each, and the pairs (rides, dollars) are (1, 4), (2, 8) and (3, 12). Predict which equation fits, c = n + 4 or c = 4n. Test both with a pair and define the variables. Explain why the other equation fails.
- In the ordered pair (x, y), which value is graphed along the horizontal axis?
- y
- Both of them
- Neither one
- x
- A table pairs x = 1, 2, 3 with y = 3, 6, 9. Which ordered pair is in the table?
- (2, 6)
- (2, 3)
- (3, 2)
- (6, 2)
- On a graph of hours worked and money earned, which axis shows the independent variable?
- The vertical axis
- The horizontal axis
- Either axis works
- Neither axis
- 1 fresh problem with new numbers each time (interactive only).
Stage 2 of 5Etapa 2 de 5
Try ItInténtalo
Use the hints when you need them. Every wrong answer tells you why.
Usa las pistas cuando las necesites. Cada respuesta incorrecta te dice por qué.
- Recreation World charges $24.95 per month. What is the total cost of 2 months of membership?
- $24.95
- $26.95
- $49.90
- $74.85
- In the equation c = 24.95m for the gym membership, what does m represent?
- The number of months of membership
- The total cost in dollars
- The monthly fee of $24.95
- The name of the gym
- A canoe rents for $15 per hour. Let h = hours and c = total cost. Which equation represents the relationship?
- c = 15h
- c = 15 + h
- h = 15c
- c = h − 15
Stage 3 of 5Etapa 3 de 5
On Your OwnPor tu cuenta
Tables, mistakes to find, and problems with a few steps.
Tablas, errores por encontrar y problemas de varios pasos.
- Using c = 24.95m, what is the total cost of 10 months of membership?
- $34.95
- $224.55
- $249.50
- $2,495.00
- Using c = 15h, what is the total cost of a 5-hour canoe rental?
- $20
- $60
- $75
- $80
- A table pairs months with total cost: (1, 24.95), (2, 49.90), (4, 99.80). Which equation matches the table, with m = months and c = cost?
- c = 24.95m
- c = m + 24.95
- m = 24.95 + c
- c = 49.90m
- What is the best next move?
- Write s = w + 6, because 1 + 6 = 7 in the first row.
- Find the weekly rate; use s = rate × w.
- Write w = 7s.
- Write s = 28w, using the last row's savings as the rate.
Stage 4 of 5Etapa 4 de 5 · OptionalOpcional
Practice MorePractica más
Optional extra practice. Press New numbers for another problem on the same skill.
Práctica extra opcional. Toca Números nuevos para otro problema de la misma habilidad.
- 6 fresh problems with new numbers each time (interactive only).
Stage 5 of 5Etapa 5 de 5
Show What You KnowDemuestra lo que sabes
Show what you learned today. Take your time; you can try again.
Muestra lo que aprendiste hoy. Tómate tu tiempo; puedes intentarlo otra vez.
- In Diamond's situation, what should be the independent variable in both equations?
- the total cost
- the price per song
- the type of service (purchase or stream)
- the number of songs
- Why does Diamond need TWO separate equations instead of one equation for both options?
- Purchasing and streaming likely follow different cost rules (such as a per-song price vs. a flat rate), so each relationship between songs and cost is different
- The number of songs is different for each option
- One equation can only have one variable
- Streaming has no relationship between songs and cost
- Once Diamond has both equations, how does she use them to decide which option is better?
- Add the two equations together to find one combined cost
- Pick whichever equation has the smaller numbers written in it, without solving anything
- Substitute the same number of songs into both equations and compare the two total costs
- Graph only one equation and assume the other follows the same line