Math Problem Statement
What is the rate of change of y with respect to x?
Solution
In the provided table, we see the relationship between variables and . The values of remain constant at 2, while the values of change.
Since the value of does not change as changes, this indicates a horizontal line. The rate of change (or slope) of a horizontal line is always 0, because the change in is zero, no matter how much changes.
The correct choice is "no slope."
If you want further details or clarification, feel free to ask!
Here are some related questions to extend your understanding:
- How do you calculate the slope between two points?
- What does it mean when a line has an undefined slope?
- How can you identify a vertical line using a table of values?
- What is the equation of a horizontal line passing through ?
- How does the slope relate to the rate of change in real-world scenarios?
Tip: The slope of a line is calculated by , where is the change in and is the change in .
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Rate of Change
Slope
Formulas
Slope formula: m = Δy / Δx
Theorems
Constant Slope Theorem
Suitable Grade Level
Grades 7-9