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The x-intercept of a linear equation is where the line crosses the x-axis. This means at this point, the value of y is zero.
To find the x-intercept, you set y equal to zero in the equation and solve for x.

For example, in the equation \( x + 5y = 0 \), you would make y=0, so it becomes:
\[ x + 5(0) = 0 \]
This simplifies to \( x = 0 \).

Therefore, the x-intercept is (0, 0). It's the point where the line touches or crosses the x-axis. Understanding this helps you plot your graph accurately.

The y-intercept of a linear equation is where the line crosses the y-axis. At this point, the value of x is zero.
To find the y-intercept, you set x equal to zero in the equation and solve for y.

For example, in the equation \( x + 5y = 0 \), you would make x=0, so it becomes:
\[ 0 + 5y = 0 \]
This simplifies to \( y = 0 \).

Therefore, the y-intercept is (0, 0). Just like with the x-intercept, the y-intercept is another essential point that helps you graph the equation correctly.
Often, the y-intercept gives you a starting point for drawing your graph.

The coordinate plane is a two-dimensional surface formed by two perpendicular number lines: the x-axis (horizontal) and the y-axis (vertical).
Every point on this plane is defined by a pair of coordinates \((x, y)\).
The origin, where these axes intersect, is \((0, 0)\).

In the context of our example equation \( x + 5y = 0 \), both intercepts are at the origin:

• The x-intercept is (0, 0)
• The y-intercept is (0, 0)

To draw the graph, you'll plot these intercepts first. Since our intercepts coincide, the line passes through the origin. Choosing another point, like (1, -0.2), aids in accurately drawing the line.
Remember, each point you plot should satisfy the equation.
Connect these points with a straight line to visualize the graph.
This visual representation shows all solutions to the equation clearly.