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To find the cost of a taxi ride after 24 minutes using the graph, we first need to determine the rate of change (slope) based on the given data.

### Step 1: Find the slope (rate of cost per minute)
From the graph:
- At 0 minutes, the cost is $3.
- At 12 minutes, the cost is $18.

The slope $ m $ can be calculated using:
\[
m = \frac{\text{Change in cost}}{\text{Change in time}} = \frac{18 - 3}{12 - 0} = \frac{15}{12} = 1.25 \text{ dollars per minute}
\]

### Step 2: Find the cost equation
The equation of a line is given by:
\[
\text{Cost} = m \cdot x + b
\]
where $ m $ is the slope (1.25), $ x $ is the time in minutes, and $ b $ is the initial cost at 0 minutes, which is $3.

Thus, the cost equation becomes:
\[
\text{Cost} = 1.25x + 3
\]

### Step 3: Calculate the cost for 24 minutes
Substitute $ x = 24 $ into the equation:
\[
\text{Cost} = 1.25(24) + 3 = 30 + 3 = 33
\]

The cost of the taxi ride after 24 minutes is $33.

Would you like more details or have any questions?

Here are five related questions to expand on the topic:
1. What would be the cost of the taxi ride after 15 minutes?
2. How would the equation change if the initial fee was $5 instead of $3?
3. What does the slope of the line represent in the context of this problem?
4. How would the graph look if the cost per minute doubled?
5. Can you find the time when the total cost reaches $25?

**Tip:** To solve problems involving linear graphs, always identify the slope and the y-intercept, as they help form the equation of the line.

The graph shows the cost in dollars for a taxi cab ride in x number of minutes. How much does the ride cost after 24 minutes?

Learn how to determine the cost of a taxi ride after 24 minutes by interpreting a graph and using the slope-intercept form of a linear equation. Suitable for middle school students in Grades 6-8.

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