Steps to Graph Using Intercepts

1. Identify the Equation: Start with the linear equation in standard form, typically written as \(Ax + By = C\).
2. Find the X-Intercept:

• Set \(y = 0\) in the equation and solve for \(x\).
• The x-intercept will be the point \((x, 0)\).

3. Find the Y-Intercept:

• Set \(x = 0\) in the equation and solve for \(y\).
• The y-intercept will be the point \((0, y)\).

4. Plot the Intercepts: On a graph, plot the points you found for the x-intercept and y-intercept.
5. Draw the Line: Use a ruler to draw a straight line through the two points. Extend the line in both directions and add arrows to indicate that it continues indefinitely.

Example

• Finding the X-Intercept:
• Set \(y = 0\): \(2x + 3(0) = 6\) → \(2x = 6\) → \(x = 3\).
• X-Intercept: \((3, 0)\).
• Finding the Y-Intercept:
• Set \(x = 0\): \(2(0) + 3y = 6\) → \(3y = 6\) → \(y = 2\).
• Y-Intercept: \((0, 2)\).
• Plotting: Plot the points \((3, 0)\) and \((0, 2)\) on the graph.
• Drawing the Line: Connect the two points with a straight line.

Additional Tips

• Use a Graphing Tool: Online graphing calculators like Desmos can help visualize the graph and check your work.

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• Practice with Different Equations: Try graphing various linear equations to become familiar with the process.

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• Check Your Work: Ensure that the line passes through both intercepts accurately.

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  By following these steps, you can effectively graph any linear equation using its x and y intercepts.
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