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In algebra, the x-intercept of a graph is the point where the graph crosses the x-axis. To identify this point, you need to follow a simple process. Start with your equation, such as \(6x - 9y = 18\). To find the x-intercept, you set \(y\) to zero because at the x-intercept, the value of \(y\) is always zero.
For example, substitute \(y = 0\) into the equation:

• \(6x - 9(0) = 18\)
• This simplifies to \(6x = 18\)
• Now solve for \(x\): \(x = \frac{18}{6} = 3\)

Therefore, the x-intercept is at the point \((3, 0)\). This means the graph will cross the x-axis at this exact location.

Just like finding the x-intercept, locating the y-intercept involves determining where the graph crosses the y-axis. For the y-intercept, set \(x\) to zero because at the y-intercept, \(x\) is always zero. Using the same equation, \(6x - 9y = 18\), substitute \(x = 0\).

• \(6(0) - 9y = 18\)
• This simplifies to \(-9y = 18\)
• Solve for \(y\): \(y = \frac{18}{-9} = -2\)

Thus, the y-intercept is the point \((0, -2)\). This is where the graph intersects the y-axis.

Graphing a linear equation involves plotting points that satisfy the equation and connecting them to form a straight line. After finding intercepts, you can easily graph the equation. Here's how you do it using the intercepts from the equation \(6x - 9y = 18\): Start by plotting the x-intercept \((3,0)\) and the y-intercept \((0, -2)\) on a graph. These intercepts are crucial as they determine the line's position.

Using a Checkpoint

To ensure the accuracy of your graph, choose a checkpoint, a point not on the intercepts, to validate your line. For instance, try \((2,2)\):

• Substitute \(x = 2\) and \(y = 2\) into the equation: \(6(2) - 9(2)\)
• This simplifies to \(12 - 18 = -6\)
• This does not equal 18; thus, \((2,2)\) is not on the line.

Finally connect the intercepts with a straight line. This line represents all solutions to the equation \(6x - 9y = 18\). By following these steps, you'll have a clear and accurate graph of your linear equation.