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 xx and yy. The values of yy remain constant at 2, while the values of xx change.

Since the value of yy does not change as xx changes, this indicates a horizontal line. The rate of change (or slope) of a horizontal line is always 0, because the change in yy is zero, no matter how much xx 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:

  1. How do you calculate the slope between two points?
  2. What does it mean when a line has an undefined slope?
  3. How can you identify a vertical line using a table of values?
  4. What is the equation of a horizontal line passing through y=2y = 2?
  5. How does the slope relate to the rate of change in real-world scenarios?

Tip: The slope of a line is calculated by ΔyΔx\frac{\Delta y}{\Delta x}, where Δy\Delta y is the change in yy and Δx\Delta x is the change in xx.

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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