Math Problem Statement

Use the table to answer the question. What is the unit rate of this graph?

Use the table to answer the question. What is the unit rate of this graph?

Solution

To find the unit rate from the graph, I will first determine the slope of the line. The slope represents the rate of change between yy and xx, or the "unit rate" in this context. The slope formula is:

slope=ΔyΔx=y2y1x2x1\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}

Step-by-Step Process:

  1. The line passes through the origin (0,0)(0, 0).
  2. Another point on the line is (6,6)(6, -6).

Using these two points, the slope is:

slope=6060=66=1\text{slope} = \frac{-6 - 0}{6 - 0} = \frac{-6}{6} = -1

Thus, the unit rate of the graph is 1-1, meaning for every 1 unit increase in xx, yy decreases by 1.

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:

  1. What does the negative slope of a line represent in real-world situations?
  2. How do you calculate the slope if the points are not integers?
  3. How would the graph change if the slope were positive?
  4. What is the difference between slope and unit rate in a linear equation?
  5. How do you determine if a line is steep or shallow based on its slope?

Tip: The slope is often referred to as the "rate of change," which tells us how yy changes in relation to xx.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope
Unit Rate

Formulas

Slope formula: (y2 - y1) / (x2 - x1)

Theorems

Slope Theorem

Suitable Grade Level

Grades 6-9