Question
(8) What are the coordinates of the \( x \)-intercept of the line \( x-2 y=4 \) ? \( (4,0) \) \( (-2,0) \) \( (0,-2) \) \( (0,4) \)
Ask by Schultz Goodwin. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The \( x \)-intercept is \( (4, 0) \).
Solution
To find the **\( x \)-intercept** of the line \( x - 2y = 4 \), follow these steps:
1. **Understand the \( x \)-intercept:**
- The \( x \)-intercept is the point where the line crosses the \( x \)-axis.
- At this point, the value of \( y \) is **0**.
2. **Substitute \( y = 0 \) into the equation:**
\[
x - 2(0) = 4
\]
\[
x = 4
\]
3. **Determine the coordinates:**
- Since \( x = 4 \) and \( y = 0 \), the coordinates of the \( x \)-intercept are **\( (4, 0) \)**.
**Answer:** \( (4,\,0) \)
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Simplify this solution The Deep Dive
To find the \( x \)-intercept of the line given by the equation \( x - 2y = 4 \), you set \( y = 0 \). Plugging that into the equation gives \( x - 2(0) = 4 \), which simplifies to \( x = 4 \). Therefore, the \( x \)-intercept is at the coordinates \( (4, 0) \). In this case, the coordinates of the intercept indicate where the line crosses the \( x \)-axis, letting us know the unique point that helps visualize the line's behavior. Such intercepts are crucial in graphing linear equations, as they help define the line's position in the Cartesian plane.
