How do I determine the x and y intercepts of the equation x = 4y + 8, and how do I graph these intercepts?

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Determining the X and Y Intercepts

To find the x and y intercepts of the equation x = 4y + 8, we need to follow these steps:

Finding the Y-Intercept

The y-intercept occurs when x = 0. We substitute x = 0 into the equation:

0 = 4y + 8

Now, rearranging the equation gives us:

4y = -8
y = -2

Thus, the y-intercept is (0, -2).

Finding the X-Intercept

The x-intercept occurs when y = 0. We substitute y = 0 into the equation:

x = 4(0) + 8

This simplifies to:

x = 8

Thus, the x-intercept is (8, 0).

Plotting the Intercepts

Now that we have both intercepts:

  • Y-Intercept: (0, -2)
  • X-Intercept: (8, 0)

To graph these intercepts on a coordinate plane:

  1. Plot the point (0, -2) on the y-axis.
  2. Plot the point (8, 0) on the x-axis.
  3. Draw a line connecting these two points to visualize the equation x = 4y + 8.

Conclusion

By finding the x and y intercepts, we have made it easier to graph the equation x = 4y + 8. These intercepts provide critical points that help define the behavior of the graph, and plotting them gives us a clear visual representation of the relationship between x and y.

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