A turtle is very slow and can only travel 10 yards in 5 minutes. Choose two points that lie on the line with the slope that best represents the number of yards moved per minute. 

Select TWO correct answers.


To determine the correct points that lie on the line representing the turtle's movement, we need to first calculate the **slope**, which is the rate at which the turtle moves in **yards per minute**.

### Step 1: Find the slope.
The turtle travels **10 yards in 5 minutes**, so the slope is calculated as:
\[
\text{slope} = \frac{\text{change in yards}}{\text{change in minutes}} = \frac{10 \text{ yards}}{5 \text{ minutes}} = 2 \text{ yards per minute}.
\]
This means the turtle moves **2 yards per minute**.

### Step 2: Points on the line.
The slope represents the rate of change (rise/run), meaning for every 1 minute (run), the turtle moves 2 yards (rise). The equation of the line representing this movement will have the form \( y = 2x \), where \( y \) is the distance in yards, and \( x \) is the time in minutes.

The points that satisfy this equation should have coordinates \((x, y)\) such that \( y = 2x \). 

### Possible Points:
1. **(0, 0)**: This point works because if 0 minutes have passed, the turtle has moved 0 yards. This satisfies the equation \( y = 2(0) = 0 \).
2. **(1, 2)**: In 1 minute, the turtle should have moved 2 yards, which satisfies the equation \( y = 2(1) = 2 \).
3. **(2, 4)**: In 2 minutes, the turtle moves 4 yards, which satisfies the equation \( y = 2(2) = 4 \).
4. **(3, 6)**: In 3 minutes, the turtle moves 6 yards, which satisfies the equation \( y = 2(3) = 6 \).
5. **(5, 10)**: In 5 minutes, the turtle moves 10 yards, which satisfies the equation \( y = 2(5) = 10 \).

### Conclusion:
You should select the following two points that lie on the line:
- (1, 2)
- (5, 10)

These two points correctly represent the turtle's rate of movement (2 yards per minute).

Do you need more details, or have any further questions?

### Related Questions:
1. How would the equation change if the turtle's speed doubled?
2. What would the slope be if the turtle traveled 15 yards in 5 minutes?
3. How would the graph look if the turtle stopped moving after 3 minutes?
4. What is the equation of a line with a slope of 3 yards per minute?
5. How can you calculate the slope of a line from any two points?

**Tip:** The slope of a line is always equal to the "rise over run," or the vertical change divided by the horizontal change between two points.

A turtle is very slow and can only travel 10 yards in 5 minutes. Choose two points that lie on the line with the slope that best represents the number of yards moved per minute. Select TWO correct answers.

Learn how to determine the slope and find two points on the line representing the movement of a turtle that travels 10 yards in 5 minutes. This math problem covers key concepts like slope calculation, rate of change, and interpreting linear equations. Suitable for students in Grades 6-8.

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