Interpreting Linear Models
Aligned to 8.SP.A.3 — Common Core State Standards for Mathematics.
What this lesson teaches
In a linear model y = mx + b, the slope m is the rate of change (how much y changes per unit of x) and the intercept b is the starting value when x = 0. Use the equation to make predictions.
Worked examples
Example 1
A model for plant height is y = 2x + 5, where x is weeks and y is centimeters. The slope 2 means the plant grows 2 cm per week; the intercept 5 means it started at 5 cm. After 4 weeks: y = 2(4) + 5 = 13 cm.
Example 2
A model for a taxi fare is y = 1.8x + 3, where x is miles. The 1.8 is the cost per mile and the 3 is the flat pickup fee.
Example 3
Predictions outside the data are risky. That plant model says y = 2(50) + 5 = 105 cm after 50 weeks, but real plants stop growing.
Practice questions
- In y = 3x + 10, what does the slope 3 represent if x is hours worked and y is dollars earned?
- Using y = 3x + 10, predict the earnings after 6 hours.
- A model gives cost y = 0.5x + 20 for x miles. Interpret both the slope and the intercept.
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.
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Interpretación de Modelos Lineales
En un modelo lineal y = mx + b, la pendiente m es la tasa de cambio (cuánto cambia y por cada unidad de x) y la intersección b es el valor inicial cuando x = 0. Usa la ecuación para hacer predicciones.
Ejemplo 1: Un modelo para la altura de una planta es y = 2x + 5, donde x son semanas y y son centímetros. La pendiente 2 significa que la planta crece 2 cm por semana; la intersección 5 significa que empezó en 5 cm. Después de 4 semanas: y = 2(4) + 5 = 13 cm.
Ejemplo 2: Un modelo para la tarifa de un taxi es y = 1.8x + 3, donde x son millas. El 1.8 es el costo por milla y el 3 es la tarifa fija de salida.
Ejemplo 3: Predecir fuera de los datos es riesgoso. Ese modelo de la planta dice y = 2(50) + 5 = 105 cm a las 50 semanas, pero las plantas reales dejan de crecer.
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