find the x and y intercepts for x + 2y = 4

To find the x- and y-intercepts of the equation \(x + 2y = 4\), we need to determine the points where the line crosses the x-axis and y-axis.

### X-Intercept

The x-intercept is the point where the line crosses the x-axis. At this point, \(y = 0\). So, we set \(y = 0\) in the equation and solve for \(x\):

\[ x + 2(0) = 4 \]
\[ x = 4 \]

Thus, the x-intercept is \((4, 0)\).

### Y-Intercept

The y-intercept is the point where the line crosses the y-axis. At this point, \(x = 0\). So, we set \(x = 0\) in the equation and solve for \(y\):

\[ 0 + 2y = 4 \]
\[ 2y = 4 \]
\[ y = 2 \]

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

### Summary

- **X-Intercept:** \((4, 0)\)
- **Y-Intercept:** \((0, 2)\)

Would you like more details or have any questions?

Here are 8 related questions to explore further:

1. How do you find the intercepts of a line given in standard form \(Ax + By = C\)?
2. What are the intercepts of the line \(2x - 3y = 6\)?
3. How can you graph a line using its x- and y-intercepts?
4. What are the steps to convert a standard form equation to slope-intercept form \(y = mx + b\)?
5. How do you find the slope of a line given two points?
6. What is the significance of the intercepts in real-world applications?
7. How can you determine if two lines are parallel or perpendicular using their equations?
8. What is the relationship between the slope and the intercepts of a line?

**Tip:** When finding intercepts, remember to set the opposite variable to zero and solve for the remaining variable.

Learn how to find the x and y intercepts of the linear equation x + 2y = 4 with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations and intercepts. Suitable for students in Grades 7-9.

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