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To find the x-intercept and y-intercept of the given line equation \( 2x - 4y = 8 \), we will follow these steps:

### Finding the x-intercept
The x-intercept occurs when \( y = 0 \). Substitute \( y = 0 \) into the equation and solve for \( x \):

\[ 2x - 4(0) = 8 \]
\[ 2x = 8 \]
\[ x = 4 \]

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

### Finding the y-intercept
The y-intercept occurs when \( x = 0 \). Substitute \( x = 0 \) into the equation and solve for \( y \):

\[ 2(0) - 4y = 8 \]
\[ -4y = 8 \]
\[ y = -2 \]

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

### Graphing the Line
Using the intercepts found, we can graph the line by plotting the points \( (4, 0) \) and \( (0, -2) \) and then drawing a straight line through these points.

Would you like a detailed graphical representation of the line, or do you have any questions about the process?

### Related Questions:
1. How do you find the slope of the line from the given equation?
2. Can you convert the given equation to slope-intercept form \( y = mx + b \)?
3. What is the distance between the x-intercept and y-intercept?
4. How would you find the x-intercept and y-intercept if the equation were in a different form, such as point-slope form?
5. How can you check if a point lies on the line given by the equation \( 2x - 4y = 8 \)?

### Tip:
When finding intercepts, remember that the x-intercept is found by setting \( y = 0 \) and solving for \( x \), while the y-intercept is found by setting \( x = 0 \) and solving for \( y \).

Find the x-intercept and the y-intercept of the line with the equation 2x - 4y = 8, and graph the line.

Learn how to find the x-intercept and y-intercept for the equation 2x - 4y = 8 and how to graph the resulting line. This tutorial covers fundamental concepts in algebra and graphing linear equations, suitable for students in Grades 8-10.

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