Slope and Intercept in Data
Aligned to S-ID.C.7 — Common Core State Standards for Mathematics.
What this lesson teaches
In a line of best fit y = mx + b, the slope m is the predicted change in y for each 1-unit increase in x, and the intercept b is the predicted y when x = 0.
Worked examples
Example 1
A model for plant height is y = 2x + 5, where x is weeks. The slope 2 means the plant grows about 2 cm per week, and the intercept 5 means it started at about 5 cm.
Example 2
A slope of −0.8 in a model of price versus age means the value falls about $0.80 per unit of age.
Example 3
The intercept is only meaningful if x = 0 is inside the data. A plant's height at week zero is; a person's weight at height zero is not.
Practice questions
- In y = 0.5x + 10 for savings over weeks, interpret the slope.
- In that same model, interpret the intercept 10.
- A model for temperature is y = −3x + 40. What does the slope −3 mean?
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
Pendiente e Intersección en los Datos
En una recta de mejor ajuste y = mx + b, la pendiente m es el cambio predicho en y por cada aumento de 1 unidad en x, y la intersección b es el valor predicho de y cuando x = 0.
Ejemplo 1: Un modelo para la altura de una planta es y = 2x + 5, donde x son semanas. La pendiente 2 significa que la planta crece unos 2 cm por semana, y la intersección 5 significa que empezó en unos 5 cm.
Ejemplo 2: Una pendiente de −0.8 en un modelo de precio contra antigüedad significa que el valor baja unos $0.80 por unidad de antigüedad.
Ejemplo 3: La intersección solo significa algo si x = 0 está dentro de los datos. La altura de una planta en la semana cero sí; el peso de una persona con estatura cero no.
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