How to Model Snow Melting with Linear Equations

TL;DR

To model the melting snow, start with an initial amount of 12 inches and decrease it by 2 inches for each day. The linear equation is y = 12 - 2x, where x represents the days after Monday and y is the inches of snow remaining. Graphing this will show a straight line reflecting the decrease in snow over the week.

Transcript

On Monday morning, there were 12 inches of snow on the ground. The weather warmed up, and by Tuesday morning, 2 inches had melted. All right, so we'll have 10 left. 2 more inches melted by Wednesday morning. This pattern continued throughout the week until no more snow was left. So they're essentially saying that we had 12 inches of snow on the gro... Read More

Key Insights

• 🫠 The melting of snow over time can be represented by a linear equation and graph.
• 🫠 The initial amount of snow on the ground and the daily melt rate determine the equation parameters.
• 📈 The graph visually depicts the decreasing trend of snow as the days progress.

Questions & Answers

Q: What is the initial amount of snow on the ground and how much melt occurs each day?

The initial amount of snow on the ground is 12 inches on Monday. Each day, 2 inches of snow melts.

Q: How can the relationship between the day and the amount of snow on the ground be represented mathematically?

The relationship can be represented by the equation y = 12 - 2x, where x is the number of days after Monday and y is the amount of snow on the ground.

Q: What happens to the amount of snow on Wednesday?

On Wednesday, which is 2 days after Monday, there will be 8 inches of snow left on the ground.

Q: What does the graph of the snow melting pattern look like?

The graph shows a linear relationship, with the amount of snow decreasing by 2 inches each day. It forms a downward-sloping straight line.

Summary & Key Takeaways

• The content discusses the process of snow melting over the course of a week, with 12 inches of snow on Monday and a daily melt of 2 inches.

• An equation is created to represent the relationship between the number of days after Monday (x) and the amount of snow on the ground (y).

• A graph is plotted to visualize the relationship, showing a linear decrease in the amount of snow as days progress.