**Title: Understanding Slope, y-intercept, and Equations**### Problems and Solutions#### Problem 1: The race begins at a rate of 1.5 meters per second. What distance, $ d $, is covered after $ t $ seconds?- **Slope**: - **y-intercept**: - **Equation**: #### Problem 2:Fifty azalea plants arrive at a florist's shop on the first day of the week. After that, they arrive at an average of 75 plants per day. How many plants will be at the shop after $ t $ days?- **Slope**: - **y-intercept**: - **Equation**: ---The equations used to solve these problems identify the rate of change (slope) and initial amount (y-intercept) to determine outcomes over a specified period or quantity. Each scenario will involve plotting variables that help in understanding these linear relationships.**Note**: For further understanding, it may be beneficial to create and analyze graphs representing these equations.*(Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.)*Page 92

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1. The race begins at a rate of 1.5 meters per second. What distance, d, is covered after t seconds? Slope y-intercept: Equation:

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**Title: Understanding Slope, y-intercept, and Equations**

### Problems and Solutions

#### Problem 1:
The race begins at a rate of 1.5 meters per second. What distance, $ d $, is covered after $ t $ seconds?

- **Slope**:
- **y-intercept**:
- **Equation**:

#### Problem 2:
Fifty azalea plants arrive at a florist's shop on the first day of the week. After that, they arrive at an average of 75 plants per day. How many plants will be at the shop after $ t $ days?

- **Slope**:
- **y-intercept**:
- **Equation**:

---

The equations used to solve these problems identify the rate of change (slope) and initial amount (y-intercept) to determine outcomes over a specified period or quantity. Each scenario will involve plotting variables that help in understanding these linear relationships.

**Note**: For further understanding, it may be beneficial to create and analyze graphs representing these equations.

*(Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.)*

Page 92

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