create a table with the rate of change as - 3/5

To create a table with a rate of change of \(-\frac{3}{5}\), we set up a linear function. Let's assume the function is in the form:

\[
y = mx + b
\]

where \(m\) is the rate of change, or slope, and \(b\) is the y-intercept. Given \(m = -\frac{3}{5}\), the equation becomes:

\[
y = -\frac{3}{5}x + b
\]

I'll create a table using different values of \(x\) (for simplicity, starting from 0) and assuming \(b = 0\) (which means the line passes through the origin). Here’s the table:

| \(x\) | \(y = -\frac{3}{5}x\) |
|-------|----------------------|
| 0     | 0                    |
| 1     | \(-\frac{3}{5}\)     |
| 2     | \(-\frac{6}{5}\)     |
| 3     | \(-\frac{9}{5}\)     |
| 4     | \(-\frac{12}{5}\)    |

The rate of change \(-\frac{3}{5}\) remains consistent, showing that as \(x\) increases by 1, \(y\) decreases by \(\frac{3}{5}\).

Would you like to explore this further, or do you have any questions?

Here are some related questions for further exploration:
1. What would the table look like if the rate of change was positive \(\frac{3}{5}\)?
2. How would the table change if we modified the y-intercept (\(b\))?
3. Can we interpret the rate of change as a real-world scenario, such as speed or temperature change?
4. How does changing the slope affect the graph of the line?
5. What happens if the slope is zero? What kind of line would that create?

**Tip:** In linear equations, the rate of change (slope) is the amount the \(y\)-value changes for each unit increase in \(x\). It helps determine how steep or flat the line is.

Create a table with the rate of change as -3/5.

Learn how to create a table using the linear equation y = -3/5x to represent a constant rate of change. This example shows the relationship between x and y values, where the rate of change is -3/5. Suitable for students in Grades 6-8 studying linear equations.

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