Question
Determine the x-intercept of the line represented by the equation \( 2x - 5y = 10 \).
Ask by Chan Harris. in South Africa
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The x-intercept of the line \( 2x - 5y = 10 \) is \( (5, 0) \).
Solution
To find the **x-intercept** of the line represented by the equation \( 2x - 5y = 10 \), 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. **Set \( y = 0 \) in the equation:**
\[
2x - 5(0) = 10
\]
\[
2x = 10
\]
3. **Solve for \( x \):**
\[
x = \frac{10}{2} = 5
\]
4. **Express the x-intercept as a point:**
\[
(5, 0)
\]
**Therefore, the x-intercept of the line \( 2x - 5y = 10 \) is \( (5, 0) \).**
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Simplify this solution Beyond the Answer
To find the x-intercept of the line represented by the equation \( 2x - 5y = 10 \), we set \( y = 0 \) and solve for \( x \). Substituting \( y = 0 \) into the equation: \[ 2x - 5(0) = 10 \] \[ 2x = 10 \] \[ x = \frac{10}{2} \] \[ x = 5 \] So, the x-intercept of the line is at the point \( (5, 0) \). Now you know where the line hits the x-axis, which is pretty handy for graphing! You can easily plot that point, and from there, you have a starting line to draw this straight road of numbers!
