91Ó°ÊÓ

Understanding the concept of the x-intercept is very important when solving linear equations. The x-intercept is the point at which a line crosses the x-axis. At this point, the y-coordinate is always zero. In other words, for any line on a graph, the x-intercept is where the line meets the x-axis. To find the x-intercept, you replace y with 0 in the equation of the line and solve for x.
This will give you the x-coordinate of the point where the line touches the x-axis.
Example: For the equation \(x - 5y = 20\), you set \(y = 0\) and solvethe equation:
\[ x - 5(0) = 20 \]
This simplifies to \( x = 20 \).
The x-intercept is then (20, 0).
Remember, the x-intercept is always written as a point (x, 0).

Just like the x-intercept, the y-intercept is another crucial element in understanding how a line behaves on a graph. The y-intercept is the point where the line crosses the y-axis. At this point, the x-coordinate is always zero. To find the y-intercept, you set x to 0 in the equation and solve for y.
This gives you the y-coordinate of the point where the line touches the y-axis.
Example: For the equation \(x - 5y = 20\), you set \(x = 0\) and solve the equation:
\[ 0 - 5y = 20 \]
This simplifies to \( -5y = 20 \). Dividing both sides by -5 gives:
\[ y = -4 \].
Therefore, the y-intercept is (0, -4).
Remember, the y-intercept is always written as a point (0, y).

Linear equations form the foundation of algebra and are essential to understand. These equations graph as straight lines and can be written in the form \(Ax + By = C\). To solve linear equations, you often need to find both the x-intercept and the y-intercept.
One common method to solve these equations is to isolate the variable you are solving for by rearranging the terms.
Steps to solve linear equations:

• Identify the equation of the line.
• To find the x-intercept, set y = 0 and solve for x.
• To find the y-intercept, set x = 0 and solve for y.

Solving for intercepts helps you to graph the line accurately, showing where the line crosses both the x and y axes.
Understanding these steps and the role of intercepts will make it easier to solve other algebraic problems as well.