The problem in the image is about interpreting a graph that shows the temperature of water in a fish tank as it cools over several hours. It asks for the equation of the line in the form of slope and y-intercept.

Here’s how to approach this:

1. Identifying the Slope (m):

   • The slope $m$ is the rate of change of temperature with respect to time. From the graph, pick two points where the line crosses grid points clearly.
   • Slope formula: $m = \frac{\Delta y}{\Delta x} = \frac{\text{change in temperature}}{\text{change in time}}$

2. Identifying the y-intercept (b):

   • The y-intercept $b$ is where the line crosses the temperature axis (vertical axis). This represents the temperature of the water at time $t = 0$.

Let me analyze the image more closely for specific points. Based on the visibility:

• Slope Calculation: Choose two points from the graph (for example, $(0, 90)$ and $(10, 40)$). The slope can be calculated as: $m = \frac{40 - 90}{10 - 0} = \frac{-50}{10} = -5$ So, the slope is $-5$.

• y-intercept: The graph shows that the line crosses the y-axis at $90$, so $b = 90$.

Thus, the equation of the line is: $y = -5x + 90$

Now, let's look at the multiple-choice options:

• Option D: $m = -5, b = 90$ matches the correct slope and y-intercept.

So, the correct answer is D.

Do you want further details or have any questions?

Here are 5 related questions to expand on this topic:

1. What is the significance of the slope in the context of cooling water temperature?
2. How would the graph look if the temperature decreased more slowly?
3. How does changing the y-intercept affect the graph of a line?
4. Can you calculate the temperature at a specific time using the equation of the line?
5. What does a slope of zero represent in terms of temperature change?

Tip: When analyzing graphs, always ensure to carefully choose points where the line crosses grid points exactly for precise calculations.