91Ó°ÊÓ

In mathematics, a horizontal line is a straight line that runs from left to right across the graph, parallel to the x-axis. It's defined by the fact that all points on the line have the same y-coordinate. This means the line doesn’t rise or fall; it simply extends in both directions horizontally.

For example, the equation \(y = \frac{3}{2}\) describes a horizontal line. This indicates that no matter what x-value you choose, the y-value will always be 1.5. Horizontal lines are simple to graph because they do not depend on the x-coordinate to determine their position on the graph.

In summary, if you encounter an equation in the form \(y = c\), where \(c\) is a constant, you're dealing with a horizontal line.

Solving equations is a fundamental skill in algebra that allows us to find the value of unknown variables. In this exercise, the equation given is a very basic linear equation:

• Begin by identifying the equation: \(6y = 9\).
• The next step is to isolate the variable \(y\). To do this, divide both sides by 6: \(y = \frac{9}{6}\).
• Finally, simplify the fraction to its lowest form: \(y = \frac{3}{2}\).

Completing these steps, we find \(y = 1.5\), which is the constant y-coordinate of the horizontal line. Understanding how to solve such basic equations is crucial because it's a building block for solving more complex mathematical problems.

Effective graphing techniques are essential for accurately representing equations on a coordinate plane. Here, let's talk about how to graph a horizontal line from an equation like \(y = \frac{3}{2}\).

First, recognize that this equation describes a horizontal line, as discussed earlier. The primary task in graphing it is identifying the constant y-coordinate:

• Begin by finding the y-coordinate on the graph; for this equation, it’s 1.5.
• Locate this point along the y-axis. For the equation \(y = \frac{3}{2}\), you would find 1.5 on the y-axis (between 1 and 2).
• Draw a straight line that passes through this point, extending it in both the positive and negative x-directions. This showcases all x-values having the y-coordinate of 1.5.

The line should be neat, level, and span the entire graph space. Practicing with simple equations like these helps build the foundation for graphing more complex equations accurately.