91Ó°ÊÓ

To understand what an x-intercept is, imagine where a straight line crosses the x-axis on a graph. This point is called the x-intercept. To find this intercept, you set the value of y to 0 in the equation of the line.

Let's look at the example equation: \(4x - 5y = 0\). To find the x-intercept, we set \(y = 0\). Now the equation becomes \(4x - 5(0) = 0\). Simplifying this, you get \(4x = 0\), which means \(x = 0\).

Therefore, the x-intercept for this equation is at the point \((0, 0)\). This means the line crosses the x-axis at the origin.

The y-intercept is where the line crosses the y-axis. To find the y-intercept, we set the value of x to 0 in the equation of the line.

Using our example \(4x - 5y = 0\), we set \(x = 0\). The equation then becomes \(4(0) - 5y = 0\). Simplifying, you get \(-5y = 0\), which results in \(y = 0\).

So, the y-intercept for this equation is at the point \((0, 0)\). This shows the line also crosses the y-axis at the origin.

Graphing linear equations involves plotting points where the line crosses the x-axis and y-axis, known as intercepts. To graph a linear equation, you typically find both the x-intercept and the y-intercept:

1. Set \(y = 0\) to find the x-intercept.
2. Set \(x = 0\) to find the y-intercept.

For our equation \(4x - 5y = 0\), we found both intercepts at \((0, 0)\). To graph this, you could plot additional points by choosing other values for x or y and solving the equation. However, because both intercepts are the same, the graph will be just a point at the origin for this specific case. For other equations, you generally get a straight line by connecting at least two points.

Understanding how to find and graph intercepts makes it easier to visualize and analyze linear relationships in algebra.