91Ó°ÊÓ

The x-intercept is the point where a graph crosses the x-axis. To find this point, we need to set y to 0 in the equation and solve for x. For example, if we have the linear equation \(x + 5y = 0\), we set y to 0 and solve for x as follows:
\
x + 5(0) = 0\
\
x = 0\
This tells us that the x-intercept occurs at the point (0, 0). This means the graph crosses the x-axis at this point.

The y-intercept is where the graph crosses the y-axis. Here, we set x to 0 in the equation and solve for y. Using the same linear equation \(x + 5y = 0\), we set x to 0 and solve for y as follows:
\
0 + 5y = 0\
\
5y = 0\
\
y = 0\
This tells us that the y-intercept occurs at the point (0, 0). This indicates that the graph crosses the y-axis at this point.

Graphing a linear equation involves plotting points and drawing a line through them. The equation \(x + 5y = 0\) has both its x-intercept and y-intercept at (0, 0).
Because a single point isn’t enough to draw a line, we need at least one more point. We can find another point by choosing a value for either x or y and solving for the corresponding variable.
For instance, let’s choose y = 1:
\
x + 5(1) = 0\
\
x + 5 = 0\
\
x = -5\
We now have another point, (-5, 1). Plotting the points (0, 0) and (-5, 1), we draw a straight line through them. This line represents the linear equation \(x + 5y = 0\). The line will continue through these points in both directions on the graph. Keep in mind that linear equations always produce straight lines.