The problem in the image states that the graph shows the amount of charge left on the computer, $C$, after being awake for $h$ hours.

Analyzing the Graph

• The graph depicts a line with a negative slope, starting from $(0, 100)$ and ending at $(5, 0)$. This means at 0 hours (starting point), the computer has 100% charge, and at 5 hours, the charge depletes to 0%.

Determining the Equation

We can identify the line equation in the form $C = mh + b$, where:

• $m$ is the slope, and
• $b$ is the y-intercept.

Step 1: Find the slope $m$

The slope formula between two points, $(h_1, C_1)$ and $(h_2, C_2)$, is given by:

$m = \frac{C_2 - C_1}{h_2 - h_1}$

Here, we have the points $(0, 100)$ and $(5, 0)$. Plugging these into the slope formula:

$m = \frac{0 - 100}{5 - 0} = \frac{-100}{5} = -20$

Step 2: Write the equation using the slope and y-intercept

Since the y-intercept ($b$) is 100, the equation is:

$C = -20h + 100$

Final Answer

The equation that describes the relationship between $C$ and $h$ is:

$C = -20h + 100$

Would you like further clarification or more details on any part of this solution? Here are some related questions to explore:

1. How do you determine the slope from a graph if it is not clearly marked?
2. What does the slope of this line indicate about the computer's battery life?
3. How can you verify the y-intercept value using the graph?
4. What would happen to the equation if the computer's initial charge was different?
5. How would you find the equation if you were given two points not at the intercepts?

Tip: When finding the slope, always ensure that you correctly identify and subtract the coordinates in the right order to avoid mistakes!