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In the image, Darren's machine requires 5 megawatts of electricity for each year he wants to travel back in time. The relationship between the years (x) and the electricity used (y, in megawatts) is proportional.

From the problem, we are told that the machine needs 5 megawatts of electricity for every year of travel. This means the equation representing the relationship is \( y = 5x \), where:

- \( y \) is the amount of electricity (in megawatts),
- \( x \) is the number of years Darren wants to travel back.

The slope of this line is the rate of change in electricity per year. Since the machine uses 5 megawatts per year, the slope \( m \) of the line is:

\[
m = \frac{\Delta y}{\Delta x} = 5
\]

Thus, the **slope of the line is 5**. This indicates that for every year Darren wants to travel back, his machine requires 5 additional megawatts of electricity.

Would you like more details, or do you have any other questions?

Here are 5 related questions you might find helpful:
1. How do you calculate the slope of a line given two points?
2. What is the equation of a line given its slope and a point?
3. How do proportional relationships differ from other linear relationships?
4. What is the significance of the y-intercept in linear equations like this?
5. How can you graph proportional relationships more accurately?

**Tip**: The slope is often a measure of "per unit" change—here, it shows the change in electricity usage per year!

There is a proportional relationship between how many years Darren wants to travel back in time, x, and how much electricity (in megawatts) his time machine needs, y. Graph this relationship and determine the slope of the line.

Learn how to calculate the slope for a proportional relationship where Darren's time machine requires 5 megawatts of electricity for each year of time travel. This problem explores key concepts such as linear equations, proportionality, and slope calculations, suitable for middle school students in Grades 6-8.

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