Question
The Chapman family is taking a road trip to Oregon this summer. Mr. Chapman plans to drive at least 150 miles each day.
Let m represent the number of miles that Mr. Chapman might drive in a day. Which inequality models the story?
Graph the inequality that models the story.
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.
Let m represent the number of miles that Mr. Chapman might drive in a day. Which inequality models the story?
Graph the inequality that models the story.
To draw a ray, plot an endpoint and select an arrow. Select an endpoint to change it from closed to open. Select the middle of the ray to delete it.
Answers
GPT-4o mini
To model the story of Mr. Chapman planning to drive at least 150 miles each day with the variable \( m \) representing the number of miles driven in a day, we can express this relationship with an inequality:
\[
m \geq 150
\]
This inequality represents that the miles driven \( m \) are greater than or equal to 150.
### Graphing the Inequality:
1. **Identify the endpoint**: The critical point in this inequality is 150.
2. **Plot the endpoint**: Since the inequality includes "at least" which is represented by "greater than or equal to," we will use a closed dot at 150.
3. **Draw the ray**: Draw a ray to the right of the point 150 on the number line to indicate all values greater than 150.
Here’s how to complete the graph:
- **Plot the point** at \( 150 \): Place a closed dot at \( 150 \) to represent that 150 is included in the possible values.
- **Draw a ray** extending to the right toward positive infinity to represent all values of \( m \) that are greater than 150.
This visually indicates that Mr. Chapman could drive 150 miles or more each day during their trip, which is consistent with the inequality \( m \geq 150 \).
\[
m \geq 150
\]
This inequality represents that the miles driven \( m \) are greater than or equal to 150.
### Graphing the Inequality:
1. **Identify the endpoint**: The critical point in this inequality is 150.
2. **Plot the endpoint**: Since the inequality includes "at least" which is represented by "greater than or equal to," we will use a closed dot at 150.
3. **Draw the ray**: Draw a ray to the right of the point 150 on the number line to indicate all values greater than 150.
Here’s how to complete the graph:
- **Plot the point** at \( 150 \): Place a closed dot at \( 150 \) to represent that 150 is included in the possible values.
- **Draw a ray** extending to the right toward positive infinity to represent all values of \( m \) that are greater than 150.
This visually indicates that Mr. Chapman could drive 150 miles or more each day during their trip, which is consistent with the inequality \( m \geq 150 \).