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. $$y=\frac{3}{2 x}$$

Short answer

The table of values yields \((x, y)\) coordinates of \((1, 1.5), (2, 0.75), (3, 0.5), (4, 0.375)\). After sketching the graph, it can be concluded that \(x\) and \(y\) are inversely proportional because \(y\) decreases as \(x\) increases.

Step-by-step solution

Create a Table of Values

Take the given equation \(y = \frac{3}{2x}\) and plug in the values of x as 1, 2, 3, and 4 to find the corresponding y-values. This will create a table of \(x, y)\) coordinates.

Sketch the Graph

Plot the points from the table on a coordinate system and connect the points to get the graph of the equation \(y = \frac{3}{2x}\).

Determine the Relationship

Examine the graph and the equation. If y decreases as \(x\) increases, and the equation takes the form \(y = \frac{k}{x}\), where \(k\) is a constant (in this case 3/2), then \(x\) and \(y\) are inversely proportional. If \(y\) increased as \(x\) increases, they would be directly proportional. Based on the graph and the equation, \(x\) and \(y\) will be found to be inversely proportional.