Problem 68 - Introductory Algebra for College Students

Question

Describe how to graph a line using the slope and \(y\) -intercept. Provide an original example with your description.

Step-by-Step Solution

Answer

To graph a line using the slope and the \(y\) -intercept, one must first understand the meaning of slope and \(y\) -intercept. Once these values are determined from the equation, you start by drawing the \(y\) -intercept on the graph. From there, use the slope to plot the next point and then connect the points with a straight line.

Step 1: Understanding the concepts

The slope and the \(y\) -intercept are crucial elements in the equation of a line in a plane, which typically has a form \(y = mx + c\). Here, \(m\) is the slope and \(c\) is the \(y\) -intercept.

Step 2: Determine the Slope and \(y\) -intercept

Given a line equation, identify the slope and the \(y\) -intercept. For instance, if you have the equation \(y = 2x + 3\), the slope (\(m\)) is 2 and the \(y\) -intercept (\(c\)) is 3.

Step 3: Draw the \(y\) -intercept on graph

Plot the \(y\) -intercept on the graph. In this example, find the point on the \(y\) -axis where \(y = 3\) and mark this point.

Step 4: Use the Slope to Determine Next Point

From the \(y\) -intercept, use the slope to find the next point. The slope is the rise over run. Since our slope is 2, this means for every 2 units rise there is 1 unit of run to the right. From the point at the \(y\) -intercept, count 2 units up and 1 unit to the right and mark this point.

Step 5: Connect the Points

Draw a straight line that passes through the two points plotted. This line represents the graph of the equation \(y = 2x + 3\).