Question

1. challenge: write an equation to describe the linear relationship between the variables \\(x\\) and \\(y\\) shown in the table.

\\(\

$$\begin{array}{|c|c|c|c|c|c|}\\hline x & 0 & 1 & 10 & 100 & 1,000 \\\\\\hline y & 0 & 0.1 & 1 & 10 & 100 \\\\\\hline\\end{array}$$

\\)

Explanation:

Calculate the constant of variation

$$ k = \frac{y}{x} = \frac{0.1}{1} = \frac{1}{10} = \frac{10}{100} = \frac{100}{1000} = 0.1 $$

Write the linear equation

$$ y = 0.1x \quad \text{or} \quad y = \frac{1}{10}x $$

Answer:

$$y = 0.1x$$