The line y = 2x+5 is reflected over the line y = x.


What is the equation of the new line?

To reflect the line \( y = 2x + 5 \) over the line \( y = x \), follow these steps:

### Step 1: Swap \( x \) and \( y \)
Since the reflection is over the line \( y = x \), you swap \( x \) and \( y \) in the original equation:

\[
x = 2y + 5
\]

### Step 2: Solve for \( y \)
Now, solve this equation for \( y \):

\[
x - 5 = 2y
\]

\[
y = \frac{x - 5}{2}
\]

Simplify it:

\[
y = \frac{1}{2}x - \frac{5}{2}
\]

### Final Answer:
The equation of the reflected line is:

\[
y = \frac{1}{2}x - \frac{5}{2}
\]

Would you like further details or have any other questions?

### Related Questions:
1. How do you reflect a line over the y-axis or x-axis?
2. How does reflecting over \( y = -x \) differ from reflecting over \( y = x \)?
3. What is the geometric interpretation of reflecting lines over other lines?
4. How do you find the point of intersection of two lines algebraically?
5. What happens to the slope of a line when it is reflected over \( y = x \)?

**Tip:** When reflecting over \( y = x \), always swap \( x \) and \( y \) in the equation.

The line y = 2x+5 is reflected over the line y = x. What is the equation of the new line?

Learn how to reflect the line y = 2x + 5 over the line y = x and find the equation of the new line. This solution includes algebraic steps such as swapping x and y, and solving for y. Suitable for students in Grades 9-11.

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