Question

Make a table of values for x = 1, 2, 3, and 4. Use the table to sketch a graph. Decide whether x and y vary directly or inversely. $$y=\frac{4}{x}$$

Short answer

The corresponding \(y\) values for \(x = 1, 2, 3, 4\) are 4, 2, \(\frac{4}{3}\), and 1, respectively. The graph, derived from these values, is a hyperbola indicating that \(x\) and \(y\) vary inversely.

Step-by-step solution

Create a Table of Values for the Equation

First, substitute the given values for \(x\) (1, 2, 3, and 4) into the equation \(y = \frac{4}{x}\) to find the corresponding \(y\) values.

Complete the Table of Values

After substituting the given \(x\) values, the resulting table will look like this: \(x=1, y=4\); \(x=2, y=2\); \(x=3, y=\frac{4}{3}\); and \(x=4, y=1\).

Draw The Graph

Use the completed table of values to draw a graph. Plot each pair of values (\(x\), \(y\)) such that \(x\) is on the horizontal axis and \(y\) is on the vertical axis. Join the points and extend the lines as necessary. Do remember that the graph of an inversely proportional function is a hyperbola, and it would never touch or cross the x and y-axes.

Determine Whether \(x\) and \(y\) Vary Directly or Inversely

Based on the equation \(y = \frac{4}{x}\), where \(y\) is equal to a constant divided by \(x\), it can be concluded that \(x\) and \(y\) vary inversely, not directly.