put the two equations y = 3 + 2x and y=5+2x in a graph

Here is the graph of the two equations \( y = 3 + 2x \) (in blue) and \( y = 5 + 2x \) (in red). 

As you can see, both lines are parallel since they have the same slope (2), but they have different y-intercepts (3 and 5). This means the lines will never intersect.

Would you like more details or have any questions?

Here are some related questions you might explore:
1. What happens if the slope of one line changes?
2. How can you determine the point of intersection if the lines were not parallel?
3. What is the significance of the y-intercept in a linear equation?
4. How do you find the distance between two parallel lines?
5. What if we added a quadratic function to this graph?

**Tip:** Parallel lines have the same slope but different y-intercepts. This characteristic makes them never intersect.

Explore the graphing of linear equations y = 3 + 2x (in blue) and y = 5 + 2x (in red). Understand how parallel lines with the same slope (2) and different y-intercepts (3 and 5) behave on a graph. Suitable for Grades 7-9.

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