https://file.aiquickdraw.com/mathbot/file/172911998683276f3caha.jpg

To identify the rate of change for a linear function from a table, we need to calculate the slope, which is given by the formula:

\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's compute this from the table:

For the points \((x_1, y_1) = (0, -3)\) and \((x_2, y_2) = (4, -10)\), we can plug the values into the slope formula:

\[
\text{slope} = \frac{-10 - (-3)}{4 - 0} = \frac{-10 + 3}{4} = \frac{-7}{4}
\]

Thus, the rate of change (slope) is \(-\frac{7}{4}\).

Would you like further explanation or more details?

Here are 5 follow-up questions for deeper understanding:
1. How would you interpret the rate of change in a real-world context?
2. What is the significance of a negative slope in a linear function?
3. How can you use the slope to find the equation of the line?
4. What other pairs of points from the table could you use to verify the slope?
5. How would the graph of this function look based on the rate of change?

**Tip**: The slope tells you how steep a line is and whether it increases or decreases as you move from left to right on the graph.

The table below represents a linear function. Identify the rate of change of the function.

Calculate the rate of change for a linear function from a table of values. Learn to use the slope formula to find the function's rate of change between points. This is suitable for Grades 7-9 math learners.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation