Find an equation of the reflection of the graph of Y equals 3/4 X minus one over the X axis

To reflect the equation of the graph of \( y = \frac{3}{4}x - 1 \) over the x-axis, you need to reverse the sign of the \( y \)-coordinate. This means you multiply the entire equation by \(-1\), because reflecting over the x-axis negates the value of \( y \).

Here are the steps:

1. Start with the original equation:
   \[
   y = \frac{3}{4}x - 1
   \]

2. Multiply the entire equation by \(-1\) to reflect it over the x-axis:
   \[
   -y = \frac{3}{4}x - 1
   \]

3. Simplify by solving for \( y \):
   \[
   y = -\left( \frac{3}{4}x - 1 \right)
   \]
   \[
   y = -\frac{3}{4}x + 1
   \]

So, the equation of the reflection of the graph over the x-axis is:
\[
y = -\frac{3}{4}x + 1
\]

### Would you like more details or further questions on this?

Here are some related questions to consider:

1. How do you reflect a graph over the y-axis?
2. What happens to the slope when you reflect a line over the x-axis?
3. How do you reflect a quadratic function over the x-axis?
4. Can you find the point of intersection between the original and reflected lines?
5. What would the reflection look like if it were over both the x- and y-axes?

**Tip:** When reflecting over the x-axis, only the sign of the \( y \)-value changes, not the slope.

Learn how to find the equation of the reflection of the linear graph y = 3/4x - 1 over the x-axis. This step-by-step solution covers key algebraic concepts, including reflection and linear equations. Suitable for students in Grades 8-10.

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