Ai Mi is going to drive from her house to City A without stopping. Let D represent Ai Mi's distance from City A t hours after leaving her house. A graph of D is shown below. Write an equation for D then state the slope of the graph and determine its interpretation in the context of the problem.
What is the D=
What is the slope of the function

To solve this problem, we need to interpret the given information and deduce the equation for \( D \) and the slope from the graph of distance vs. time.

### 1. Equation for \( D \)

We can assume that the relationship between distance \( D \) and time \( t \) is linear, based on the description of a graph. The general form of a linear equation is:

\[
D = mt + b
\]

where:
- \( D \) is the distance from City A,
- \( t \) is the time after Ai Mi leaves her house,
- \( m \) is the slope of the line (rate of change of distance with respect to time),
- \( b \) is the initial distance from City A (i.e., the distance when \( t = 0 \)).

#### Initial Distance:
From the context, \( b \) should be the distance from City A when Ai Mi begins her journey. This is typically shown as the y-intercept on the graph.

#### Slope \( m \):
The slope \( m \) represents the rate at which Ai Mi's distance from City A decreases with time. Since she is driving towards City A, the distance should be decreasing, which means the slope will be negative.

### 2. Interpretation of the Slope

The slope \( m \) of the graph represents Ai Mi’s speed, but with a negative sign since she is getting closer to City A as time increases. For example, if the slope is \( -50 \), it means she is approaching City A at a rate of 50 miles per hour (or whichever unit the distance is measured in).

Let me know if you would like to share the graph or any specific values from the graph for a more detailed equation.

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Do you want further clarification on these points, or do you have specific numbers from the graph?

Here are 5 relative questions for deeper exploration:
1. What units are used for distance and time in the problem?
2. What was Ai Mi's initial distance from City A?
3. How long did it take Ai Mi to reach City A?
4. Does Ai Mi's speed remain constant throughout her journey?
5. What would the graph look like if Ai Mi drove at different speeds at different times?

**Tip:** In word problems involving linear graphs, always identify the y-intercept and slope first, as they provide crucial information about initial conditions and rates of change.

Ai Mi is going to drive from her house to City A without stopping. Let D represent Ai Mi's distance from City A t hours after leaving her house. A graph of D is shown below. Write an equation for D then state the slope of the graph and determine its interpretation in the context of the problem.

Discover how to write a linear equation for Ai Mi's distance from City A as a function of time. Learn to interpret the slope of the distance-time graph, which represents Ai Mi's driving speed, and how it relates to her journey. Suitable for students in Grades 8-10.

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