Math Problem Statement

Find the rate of change using the graph.

Solution

To find the rate of change from the graph, we can treat the graph as a collection of points and use the formula for slope (rate of change), which is:

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

From the image, we can extract two points from the graph:

  1. (0,10)(0, 10)
  2. (5,0)(5, 0)

Now, let's calculate the rate of change (slope):

ΔyΔx=01050=105=2\frac{\Delta y}{\Delta x} = \frac{0 - 10}{5 - 0} = \frac{-10}{5} = -2

Thus, the rate of change is -2.

Would you like further details or clarification on this? Here are five related questions:

  1. How do you calculate the slope of a line between any two points?
  2. What is the interpretation of a negative rate of change in this graph?
  3. How does the steepness of the slope affect the rate of change?
  4. Can you explain what happens to the graph if the slope is 0?
  5. How would the rate of change differ if the points were reversed?

Tip: The rate of change represents how quickly one variable changes with respect to another, and a negative rate of change indicates a downward trend.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Rate of Change
Slope

Formulas

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

Theorems

Slope Theorem

Suitable Grade Level

Grades 6-8