The equations of five lines are given below. Line A=y=2x+3 Line B=1/2x-3 Line C=y=6-x Line D y-2x=7 Line E y+2x=3 which two lines cross the y axis at the same point?



We can identify where each line crosses the y-axis by finding the **y-intercept**. The y-intercept occurs where \( x = 0 \).

Here are the equations and their y-intercepts:

- **Line A: \( y = 2x + 3 \)**  
  When \( x = 0 \), \( y = 2(0) + 3 = 3 \).  
  **Y-intercept: 3**

- **Line B: \( y = \frac{1}{2}x - 3 \)**  
  When \( x = 0 \), \( y = \frac{1}{2}(0) - 3 = -3 \).  
  **Y-intercept: -3**

- **Line C: \( y = 6 - x \)**  
  When \( x = 0 \), \( y = 6 - 0 = 6 \).  
  **Y-intercept: 6**

- **Line D: \( y - 2x = 7 \)**  
  Rearrange to get it in slope-intercept form:  
  \( y = 2x + 7 \).  
  When \( x = 0 \), \( y = 2(0) + 7 = 7 \).  
  **Y-intercept: 7**

- **Line E: \( y + 2x = 3 \)**  
  Rearrange to get it in slope-intercept form:  
  \( y = -2x + 3 \).  
  When \( x = 0 \), \( y = -2(0) + 3 = 3 \).  
  **Y-intercept: 3**

### Conclusion:
Lines **A** and **E** cross the y-axis at the same point, which is \( y = 3 \).

Would you like any details or have any further questions?

Here are 5 questions related to this topic:

1. How do you find the slope of a line from its equation?
2. What is the significance of the y-intercept in a real-world scenario?
3. How do parallel lines behave in terms of slope and y-intercept?
4. How do we find the point of intersection between two lines?
5. What are the different forms of a linear equation?

**Tip:** Always convert equations into slope-intercept form \( y = mx + b \) to easily identify the slope and y-intercept.

Learn how to determine which two lines cross the y-axis at the same point using their equations. This problem covers linear equations, y-intercepts, and slopes. Suitable for Grades 7-9 students.

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