Lesson 1.2 Interpreting Graphs - Free Printable

Problem Analysis and Solution

The image provided contains a distance-time graph that describes Easton's movement over time. The graph shows how far Easton is from his home at different times. Let's break down the problem step by step and solve it.

#### Graph Description
- The x-axis represents time in minutes.
- The y-axis represents distance from home in miles.
- Key points on the graph:
- From \( t = 0 \) to \( t = 20 \): Distance increases linearly.
- From \( t = 20 \) to \( t = 30 \): Distance remains constant (horizontal line).
- From \( t = 30 \) to \( t = 45 \): Distance increases again.
- From \( t = 45 \) to \( t = 70 \): Distance remains constant.
- From \( t = 70 \) to \( t = 80 \): Distance decreases linearly back to 0.

#### Questions to Solve
1. How many minutes is Easton at the grocery store?
2. During what interval(s) is the distance \( d \) decreasing?
3. What does the context of this problem suggest?

---

Solution

#### 1. How many minutes is Easton at the grocery store?
- The grocery store is labeled on the graph as the segment where the distance from home is constant at its maximum value.
- This occurs between \( t = 45 \) and \( t = 70 \).
- The duration spent at the grocery store is:
\[
70 - 45 = 25 \text{ minutes}
\]

#### 2. During what interval(s) is the distance \( d \) decreasing?
- The distance \( d \) is decreasing when the slope of the graph is negative.
- From the graph, the distance decreases between \( t = 70 \) and \( t = 80 \).

#### 3. What does the context of this problem suggest?
- The graph represents Easton's journey away from and back to his home.
- Key segments of the journey:
- \( t = 0 \) to \( t = 20 \): Easton travels to the bank.
- \( t = 20 \) to \( t = 30 \): Easton stays at the bank.
- \( t = 30 \) to \( t = 45 \): Easton travels to the grocery store.
- \( t = 45 \) to \( t = 70 \): Easton stays at the grocery store.
- \( t = 70 \) to \( t = 80 \): Easton returns home.
- The context suggests a series of stops (bank and grocery store) during a round trip.

---

Final Answers

1. Easton is at the grocery store for 25 minutes.
2. The distance \( d \) is decreasing during the interval \( 70 < t < 80 \).
3. The context suggests that Easton is making a series of trips involving stops at specific locations (bank and grocery store) before returning home.

\[
\boxed{25 \text{ minutes}, 70 < t < 80, \text{Easton is making a series of trips with stops}}
\]