Math Problem Statement

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

Solution

To reflect the equation of the graph of y=34x1y = \frac{3}{4}x - 1 over the x-axis, you need to reverse the sign of the yy-coordinate. This means you multiply the entire equation by 1-1, because reflecting over the x-axis negates the value of yy.

Here are the steps:

  1. Start with the original equation: y=34x1y = \frac{3}{4}x - 1

  2. Multiply the entire equation by 1-1 to reflect it over the x-axis: y=34x1-y = \frac{3}{4}x - 1

  3. Simplify by solving for yy: y=(34x1)y = -\left( \frac{3}{4}x - 1 \right) y=34x+1y = -\frac{3}{4}x + 1

So, the equation of the reflection of the graph over the x-axis is: y=34x+1y = -\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 yy-value changes, not the slope.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Reflections over the x-axis

Formulas

y = mx + b
Reflection over the x-axis: y = -f(x)

Theorems

Reflection Theorem (across the x-axis)

Suitable Grade Level

Grades 8-10