https://file.aiquickdraw.com/mathbot/file/1730225026379fqtn0klm.jpg

To determine the rate of change (slope) from the graph provided, we can follow these steps:

### Step 1: Identify two points on the line  
From the image, two clear points on the line appear to be:  
- Point 1: \((-5, 4)\)  
- Point 2: \((5, -4)\)

### Step 2: Use the slope formula  
The slope (rate of change) \(m\) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Plugging in the coordinates from the two points:  
\((x_1, y_1) = (-5, 4)\) and \((x_2, y_2) = (5, -4)\):

\[
m = \frac{-4 - 4}{5 - (-5)} = \frac{-8}{10} = -\frac{4}{5}
\]

### Step 3: Interpret the result  
The rate of change (slope) of the function is \(-\frac{4}{5}\).

So, the correct answer is:

\[
-\frac{4}{5}
\]

Let me know if you want more details or have any questions!

---

Here are 5 related questions to deepen your understanding:
1. What does a negative slope indicate about the direction of a line?
2. How can you tell if two lines are parallel based on their slopes?
3. What would the slope be if the line were horizontal?
4. If a line passes through the origin, how does its slope affect the y-intercept?
5. How would the slope change if we switched the points in the slope calculation?

**Tip:** Remember, slope tells us how much the y-value changes for a given change in x. It helps describe the "steepness" of a line.

The graph of a function is shown on the coordinate plane below. Identify the rate of change of the function.

Learn how to identify the rate of change from a linear function's graph. This problem covers algebraic concepts, including slope calculation and the rate of change in linear equations. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation