Problem 52 - Introductory Algebra for College Students

Question

Use a graphing utility to graph \(y=1.75 x-2 .\) Select the best viewing rectangle possible by experimenting with the range settings to show that the line's slope is \(\frac{7}{4}\).

Step-by-Step Solution

Answer

By using a graphing utility to graph the given equation, and selecting right viewing rectangle for visibility of the slope, it is evident that the slope of line is indeed 1.75 or \(\frac{7}{4}\).

Step 1: Use a Graphing Utility

To begin, open a preferred graphing utility. The equation to be plotted is \(y=1.75x-2\). Plot this equation on the graph.

Step 2: Select the Viewing Rectangle

Once the line is graphed, adjust the view of the graph to clearly see the slope. This usually means changing the scale ratio between the \(x\) axis and the \(y\) axis. Make sure both axes are visible and the line stretches across the entire length of the grid for clear visibility.

Step 3: Analyze the Slope

The slope (1.75 or \(\frac{7}{4}\)) represents the change in \(y\) for every unit change in \(x\). Pick two points on the line that are easy to read, for example, where the line intersects grid lines. Calculate the rise (change in \(y\)) over run (change in \(x\)) between those two points. It should come out to be 1.75.