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 over the x-axis, you need to reverse the sign of the -coordinate. This means you multiply the entire equation by , because reflecting over the x-axis negates the value of .
Here are the steps:
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Start with the original equation:
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Multiply the entire equation by to reflect it over the x-axis:
-
Simplify by solving for :
So, the equation of the reflection of the graph over the x-axis is:
Would you like more details or further questions on this?
Here are some related questions to consider:
- How do you reflect a graph over the y-axis?
- What happens to the slope when you reflect a line over the x-axis?
- How do you reflect a quadratic function over the x-axis?
- Can you find the point of intersection between the original and reflected lines?
- 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 -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