Questions: Según el gráfico de la figura 3, x e y son magnitudes directamente proporcionales. Entonces, ¿cuál es el valor de a? A) 1/3 B) 3 C) 6 D) 9 E) 12

Solution Steps

The problem states that \( x \) and \( y \) are directly proportional, and we need to find the value of \( a \) from the given graph.

Since \( x \) and \( y \) are directly proportional, we can express this relationship as \( y = kx \), where \( k \) is the constant of proportionality.

From the graph, we can see that when \( x = 3 \), \( y = 6 \). Using these values, we can find \( k \): \[ y = kx \] \[ 6 = k \cdot 3 \] \[ k = \frac{6}{3} = 2 \]

Now that we know \( k = 2 \), we can use this to find \( a \). From the graph, \( a \) is the \( y \)-value when \( x = 1.5 \): \[ y = 2x \] \[ a = 2 \cdot 1.5 = 3 \]

Final Answer