Modeling Linear Relationships
Aligned to 8.F.B.4 — Common Core State Standards for Mathematics.
What this lesson teaches
To model a linear relationship, find the rate of change (slope) and the initial value (y-intercept), then write y = mx + b. From two points, slope = (change in y) / (change in x).
Worked example
A plumber charges a $40 fee plus $30 per hour. The initial value is b = 40 and the rate is m = 30, so y = 30x + 40. For 3 hours: y = 30(3) + 40 = $130.
Practice questions
- Write an equation: a gym costs $25 to join plus $15 per month.
- Find the equation of the line through (1, 7) and (3, 15).
- A candle is 20 cm tall and burns 4 cm per hour. Write its equation and find its height after 3 hours.
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
Modelado de Relaciones Lineales
Para modelar una relación lineal, halla la tasa de cambio (pendiente) y el valor inicial (intersección con el eje y), y luego escribe y = mx + b. A partir de dos puntos, pendiente = (cambio en y) / (cambio en x).
Ejemplo: Un plomero cobra una tarifa de $40 más $30 por hora. El valor inicial es b = 40 y la tasa es m = 30, así que y = 30x + 40. Para 3 horas: y = 30(3) + 40 = $130.
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