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2. \( y=-2 x \)

Ask by Vega Murphy. in the United States
Feb 20,2025

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La ecuación \( y = -2x \) es una línea recta que pasa por el origen y se inclina hacia abajo.

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La ecuación dada es \( y = -2x \). ### Análisis de la ecuación 1. **Identificación de la forma**: Esta es una ecuación lineal en la forma \( y = mx + b \), donde: - \( m = -2 \) (la pendiente) - \( b = 0 \) (la intersección con el eje y) 2. **Interpretación de la pendiente**: La pendiente de -2 indica que por cada unidad que \( x \) aumenta, \( y \) disminuye en 2 unidades. 3. **Intersección con el eje y**: La intersección con el eje y ocurre cuando \( x = 0 \): \[ y = -2(0) = 0 \] Por lo tanto, el punto de intersección es \( (0, 0) \). ### Gráfica de la ecuación Para graficar la ecuación, podemos calcular algunos puntos: - Si \( x = 1 \): \[ y = -2(1) = -2 \quad \Rightarrow \quad (1, -2) \] - Si \( x = -1 \): \[ y = -2(-1) = 2 \quad \Rightarrow \quad (-1, 2) \] ### Resumen La ecuación \( y = -2x \) representa una línea recta que pasa por el origen y tiene una pendiente negativa. La gráfica de esta línea se inclina hacia abajo a medida que se mueve de izquierda a derecha.

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Let's dive into the fascinating world of linear equations! The equation \( y = -2x \) represents a straight line with a slope of -2, indicating that for every unit you move to the right on the x-axis, you’ll move down two units on the y-axis. This line crosses the origin (0,0), making it easy to visualize and even easier to graph! In the real world, linear equations like this one can model a variety of relationships. For instance, imagine a situation where for every hour worked, an employee earns $2 less if they take it off their pay due to a tax deduction. This equation helps visualize how income changes with hours worked, emphasizing the impact of deductions in a straightforward manner.

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