Question

1. a. constant: b. equation: c. what does the constant mean for this situation? price of soda in a vending machine

Explanation:

Step1: Find the constant

The line passes through the origin \((0,0)\), and we can use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Taking two points \((1,2)\) and \((2,4)\), \(m=\frac{4 - 2}{2 - 1}=2\). Since it's a direct - variation (passes through the origin), the constant is \(2\).

Step2: Find the equation

The equation for direct variation is \(y = kx\), where \(k\) is the constant. Substituting \(k = 2\), the equation is \(y=2x\).

Step3: Interpret the constant

In the context of the price of soda in a vending machine, \(x\) is the number of sodas and \(y\) is the price. The constant \(k = 2\) means that each soda costs \(2\) dollars.

Answer:

a. \(2\)
b. \(y = 2x\)
c. Each soda costs \(2\) dollars.